Connelly's writing exhibits a self-deprecating humour and love of eccentricity that echoes the pioneering style of Bill Bryson. Similarly, he shares with these other named writers a fascination with subject-matter that had previously escaped the attentions of the traditional travel writing fraternity. Rather than travelling round Ireland with a fridge (Hawks) or pedalling the route of the Tour de France (Moore), Connelly's early work focused on football, from Hackney Marshes to Sarajevo and most points in between. Stamping Grounds was Connelly's breakthrough. He follows the hapless Liechtenstein national football team through a disastrous if wholly predictable World Cup qualifying campaign. They lost all eight matches without scoring a single goal, but Connelly shows that it is the taking part that counts. Along the way, he comes to understand the nature of an entire country, not least when he meets a man who married an eagle.

The bestselling Attention All Shipping (2004) was the first book not to take football as its central subject: again seeking out unusual destinations, he travels to each area of the shipping forecast made famous on BBC Radio 4. The radio station returned the favour, making Attention All Shipping their "Book of the Week" and propelling the book to the top of the sales charts. In Search of Elvis, was published in the UK in January 2007. In it, Connelly travels the globe examining the legacy of Elvis Presley, a journey that takes him to such seemingly unlikely places as Uzbekistan, Finland, and Israel, as well as Memphis, Tupelo, and Las Vegas. The associated audiobook was narrated by the actor Julian Rhind-Tutt. In 2009 his next book And Did Those Feet followed great journeys from British and Irish history and was again a BBC Radio 4 "Book of the Week".

His work has also appeared in the Guardian, the Daily Telegraph, the Times, the Scotsman, the Herald, and he was a presenter on the BBC 1 Holiday programme and has lectured at the Royal Geographical Society. He co-presented the first three series of the BBC Radio 4 programme Traveller's Tree with Fi Glover. A former professional musician, Connelly plays the ukulele and lives in Ireland.

In August 2008 Attention All Shipping was voted the second greatest audiobook of all time in a public vote organised by The Guardian newspaper and Waterstone's bookshops, finishing behind The Hitchhiker's Guide To The Galaxy.