The pair, who were Campaign Faces to Watch in 2004, join the agency from Abbott Mead Vickers BBDO.
In their new roles, they will work across the agency's clients, which include France Telecom, Sony and the BBC.
At AMV, they created the British Television Advertising Awards gold-winning "noitulove" spot for Guinness and the "fingerlegs" work for the NHS, which won a silver at the Campaign Press Awards.
Most recently, they created the National Lottery television commercial "migrate", featuring a flock of migrating bricks. They also worked on the long-running campaign for The Economist.
Doman and Heartfield first teamed up at Buckinghamshire College in the 90s. They began their careers at Ogilvy & Mather, before moving to Miles Calcraft Briginshaw Duffy and then on to AMV.
Richard Flintham, Fallon's managing partner and executive creative director, said: "We've admired Matt and Ian for some time now. It's a bit to do with their book, but mostly to do with their attitude."
Their hirings come as Fallon moves to increase its staff levels after winning France Telecom's account in March. The win led to the promotion of Juan Cabral and Micah Walker to the positions of creative directors with responsibility for Sony and Orange respectively.
At the same time, Flintham and Andy McLeod were named executive creative directors.
Farah Ramzan Golant, the AMV chief executive, added: "Matt and Ian have always been 100 per cent committed to brilliant ideas. I have no doubt we'll see much more from them."