Arriaga was born in Mexico City and spent his childhood in one of the most violent sectors of the metropolis. At the age of 13, he lost the sense of smell after a brutal street fight that would later serve as inspiration for some of his work.

Before engaging in his writing career, Arriaga tried out a variety of jobs and professions, amongst which were that of boxer, basketball player and professional soccer player. He completed a B.A. in Communications and a M.A. in Psychology at the Ibero-American University, where he taught several courses in media studies before joining the ITESM.

While teaching at the Universidad Iberoamericana, Arriaga met future film director Alejandro González Iñárritu and decided to make a feature length, multiplot film set in Mexico City. The result was Amores Perros (1999), one of the most heavily praised films in the recent history of Mexican cinema. The film, with its gritty look at the underbelly of Mexican life received an Oscar nomination for "Best Foreign Film" as well as a BAFTA Film Award for "Best Film not in the English Language," the "Critics Week Grand Prize" and "Young Critics Award" at the 2000 Cannes Film Festival as well as many other awards from festivals and societies around the world.

The success of Amores Perros earned Arriaga and Iñárritu an invitation to the U.S. to work on the Universal/Focus feature film 21 Grams, starring Benicio del Toro, Naomi Watts and Sean Penn. Watts and del Toro received Academy Award nominations for their performances.

Iñárritu and Arriaga collaborated on a third movie, Babel, to form a trilogy with his first two pictures focusing on the theme of death. However, friction between writer and director led to Iñarritu banning Arriaga from attending the 2006 Cannes screening of Babel. Nevertheless, Inarritu and Arriaga both received Academy Award nominations for their work.

On January 19, 2007, the film adaptation of his book El Búfalo de la Noche directed by Jorge Hernandez Aldana premiered at the Sundance film festival. It features an original score by Omar Rodríguez-López of The Mars Volta. The main title sequence for this movie was created by Canadian studio Mucho Motion and One Size from the Netherlands.

An award-winning screenwriter, Arriaga has repeatedly stated that he hates being called a "screenwriter" and that he hates screenplays being referred to as such. He claims that he and all other screenwriters are writers, and the title of screenwriter diminishes the work of screenwriters. He now continuously advocates for screenwriters being referred to as "writers" and screenplays being referred to as "Works of Film". However, in a TV interview at KUSI in San Diego on September 10, 2009, he clarified that he did not really mind the English word "screenwriter." It was the word in Spanish which he did not like. The Spanish word most often associated with screenwriters, "guionista", is also used to describe people who write tour guidebooks. He does not think of himself as a guidebook author.