Moffat was born in Paisley, Scotland, where he attended Camphill High School. He studied at the University of Glasgow, where he was involved with the student television station, GUST (Glasgow University Student Television). After gaining an MA degree in English from Glasgow, he worked as a teacher for three years at Cowdenknowes High School, Greenock. In the 1980s he wrote a play entitled War Zones (performed at the 1985 Glasgow Mayfest and the Edinburgh Festival Fringe) and a musical called Knifer. His father, Bill Moffat, was a head teacher at Thorn Primary School in Johnstone, Renfrewshire; when the school was used for Harry Secombe's Highway in the late 1980s, he mentioned to the producers that he had an idea for a television series about a school newspaper. The producers asked for a sample script, to which Bill Moffat agreed on condition his son write it. Producer Sandra Hastie said that it was "the best ever first script" that she had read.

The resulting series was titled Press Gang, starring Julia Sawalha and Dexter Fletcher, and ran for five series on ITV between 1989 and 1993, with Moffat writing all forty-three episodes. The programme won a BAFTA award in its second series.

During production of the second series of Press Gang, Moffat was experiencing an unhappy personal life as a result of the break-up of his first marriage. The producer was secretly phoning his friends at home to check on his state. His wife's new lover was represented in the episode "The Big Finish?" by the character Brian Magboy (Simon Schatzberger), a name inspired by Brian: Maggie's boy. Moffat brought in the character so that all sorts of unfortunate things would happen to him, such as having a typewriter dropped on his foot.

By 1990, Moffat had written two series of Press Gang, but the programme's high cost along with organisational changes at backers Central Independent Television cast its future in doubt. As Moffat wondered what to do next and worried about his future employment, Bob Spiers, Press Gang's primary director, suggested that he meet with producer Andre Ptaszynski to discuss writing a sitcom. Inspired by his experience working in education, Moffat's initial proposal was a programme similar to what would become Chalk, a sitcom set in a school that eventually aired in 1997. During the pitch meeting at the Groucho Club, Ptaszynski realised that Moffat was talking passionately about his impending divorce and suggested that he write about that instead of a school sitcom. Taking Ptaszynski's advice, Moffat's new idea was about "a sitcom writer whose wife leaves him". Moffat wrote two series of Joking Apart, which was directed by Bob Spiers, and starred Robert Bathurst and Fiona Gillies. The show won the Bronze Rose of Montreux and was entered for the Emmys. In an interview with Richard Herring, Moffat says that "The sit-com actually lasted slightly longer than my marriage." Fiona Gillies, who played the adulteress Becky, says that she was aware that some of her dialogue was based on what had been said to Moffat during his own separation. Moffat recycled his own dialogue: when he had learned that his wife's lover was a fan of Press Gang, he replied, "Well, did he have to fuck my wife? Most people just write in!". The line, with the expletive replaced by "shagged", was used in the first episode of Joking Apart.

Speaking about the autobiographical elements of the show, the writer jokes that he has to remember that his wife didn't leave him for an estate agent; his wife was an estate agent. Conversely, his later sitcom Coupling was based his relationship with his second wife, TV producer Sue Vertue. Moffat reused the surname 'Taylor', which is Mark's surname in Joking Apart, for Jack Davenport's character Steve in Coupling.

He wrote three episodes of Murder Most Horrid, an anthology series of comedic tales starring Dawn French. The first ("Overkill", directed by Bob Spiers) was identified by the BBC as a "highlight" of the series. His other two episodes were "Dying Live" (dir. Dewi Humphreys) and "Elvis, Jesus and Zack" (dir. Tony Dow).

Between marriages, Moffat claims that he "shagged [his] way round television studios like a mechanical digger." According to an interview with The New York Times, Moffat met television producer Sue Vertue at the Edinburgh Television Festival in 1996. Vertue had been working for Tiger Aspect, a production company run by Peter Bennett-Jones. Bennett-Jones and his friend and former colleague Andre Ptaszynski, who had worked with Moffat on Joking Apart, told Moffat and Vertue that each fancied the other. A relationship blossomed and they left their respective production companies to join Hartswood Films, run by Beryl Vertue, Sue's mother. The couple have two children together: Joshua and Louis.

Before Moffat left Pola Jones for Hartswood, Ptaszynski produced Chalk, the series that the writer had pitched to him at the beginning of the decade. Set in a comprehensive school and starring David Bamber as manic deputy head Eric Slatt and Nicola Walker as Suzy Travis, the show was based on Moffat's three years as an English teacher. The studio audience responded so positively to the first series when it was taped that the BBC commissioned a second series before the first had aired. However, it was met less enthusiastically by critics upon transmission, who had taken exception to the BBC's publicity department comparing the show to the highly-respected Fawlty Towers. In an interview in the early 2000s, Moffat refuses to even name the series, joking that he might get attacked in the street.

After production wrapped on Chalk in 1997, Moffat announced to the cast that he was marrying Vertue. When she eventually asked him for a sitcom, he decided to base it around the evolution of their own relationship. Coupling was first broadcast on BBC2 in 2000, with his wife producing for Hartswood Films. The series proved to be highly successful, running until 2004 and producing four series and twenty-eight episodes, all written by Moffat. He also wrote the original, unbroadcast, pilot episode for the American version of the same series, in 2003, although this was less successful and was cancelled after four episodes on the NBC network. Moffat has blamed its failure on an unprecedented level of network interference.

He wrote the Hartswood Films drama series Jekyll, a modern version of The Strange Case of Dr Jekyll and Mr Hyde, which aired on BBC One in June and July 2007. In an interview with The Age, James Nesbitt, who played the eponymous character, called Moffat "an eccentric, shy fellow", while commending his writing as "inventive and dark and funny".

In June 2007 Moffat told The Stage that he is working on a new sitcom. Provisionally titled Adam and Eve, it concerns a boss and his PA, who are long-term friends but never get together. In October 2007 it was reported that Moffat would be scripting a trilogy of The Adventures of Tintin films for directors Steven Spielberg and Peter Jackson. According to The Times newspaper, Moffat had to be "love bombed" by Spielberg into accepting the offer to write the films, with the director promising to shield him from studio interference with his writing. He had intended to complete work on the whole trilogy before resuming work on Doctor Who, but the intervening WGA strike meant he could submit a finished script for the first film only. In July 2008, Moffat was quoted by the Daily Mail as saying: "I could not work on the second Tintin film and work on Doctor Who. So I chose Doctor Who."

Moffat remains a writer for Hartswood Films even after his appointment as show-runner for Doctor Who. During their journeys from London to Cardiff for Doctor Who, Moffat and Mark Gatiss conceived a contemporary update of Sherlock Holmes, called Sherlock. Benedict Cumberbatch was cast as Holmes, with Martin Freeman as Dr Watson. A 60-minute pilot, written by Moffat, was shot in January 2009. The pilot was not broadcast, but three 90-minute episodes were commissioned. Moffat wrote the first of these, "A Study in Pink", which was broadcast on 25 July 2010 on BBC One and BBC HD.

Moffat has been a fan of Doctor Who since childhood. His first professional contribution to Doctor Who was a prose story, "Continuity Errors", which was published in the 1996 Virgin Books anthology Consequences. In 1999 he scripted the parody Doctor Who and the Curse of Fatal Death, which aired as part of Comic Relief's Red Nose Day charity telethon. The co-producer for that year's Comic Relief telethon was Moffat's then-new wife, Sue Vertue.

In 2004 Moffat was signed to write for the revival of Doctor Who. He became known, according to The Guardian, for writing "the clever, darker episodes" of the first four series of the show. His contribution for the 2005 series was the Hugo Award-winning two-part story "The Empty Child"/"The Doctor Dances". In the DVD audio commentary he says that he waited forty years to see his name appear on top of that theme music. He wrote an episode for each of the two following series of Doctor Who: "The Girl in the Fireplace" in the 2006 series (which won the 2007 Hugo Award for Best Dramatic Presentation, Short Form and was nominated for a 2006 Nebula Award) and "Blink" in the 2007 series. In the Doctor Who Magazine reader poll for the 2007 series, Moffat was voted as best writer and "Blink" as the best story. The episode was also nominated for the Nebula Award for Best Script. In 2008 it secured him his third Hugo win, again for Best Dramatic Presentation, the BAFTA Craft Award for Best Writer, and a BAFTA Cymru Award for Best Screenwriter. He also wrote the 2007 Children in Need "special scene" "Time Crash".

He wrote a two-part story for series four in 2008, titled "Silence in the Library"/"Forest of the Dead". This made Moffat and series executive producer Russell T Davies the only writers to have contributed scripts to all four series of the revived show. In March 2008, Davies said that he often rewrote scripts from other writers, but didn't "touch a word" of Moffat's episodes. Moffat's script for series four secured him his fourth consecutive Hugo Awards nomination, though it did not win.

The BBC announced in May 2008 that Moffat would be taking over from Russell T Davies as head writer and executive producer for the revived show's fifth series, to be broadcast in 2010, although Davies had initiated discussions with Moffat regarding this as far back as July 2007. Commenting on his appointment, Moffat said it was "the proper duty of every British subject to come to the aid of the TARDIS". Production on Moffat's time in charge of the programme began in July 2009. As executive producer and head writer, he was significantly involved in casting Matt Smith as the Eleventh Doctor. Smith first appeared as the Doctor at the end of Davies and David Tennant's final episode "The End of Time, Part 2", in a short post-regeneration scene that Davies left for Moffat to write himself. Moffat wrote the scene in "about ten minutes" as "a bit of fun banter" for the new Doctor.

In addition to his television episodes, Moffat has also contributed stories to Panini Publishing's Doctor Who Storybook series, penning the short stories "What I Did On My Christmas Holidays By Sally Sparrow" for the 2006 book (which later formed the basis of his TV episode "Blink"), "Corner of the Eye" for the 2007 volume and "A Letter From the Doctor" which opens the 2009 Storybook.