Doman and Heartfield created the 2006 Cannes Grand Prix-winning "noitulove" spot for Guinness while at their previous agency, Abbott Mead Vickers BBDO. They joined Fallon in July 2006, a week after they took the Grand Prix, which had been tipped to go to Fallon for its "balls" spot for Sony Bravia.
A senior Fallon source confirmed they had resigned, and added: "It's fair to say we weren't getting the best out of them, and they weren't getting the best out of us."
Doman and Heartfield are working on Fallon's campaign to advertise Eurostar's move to St Pancras in October. They are expected to join BMB when the campaign completes post-production.
Doman said: "We never intended to leave Fallon so soon, but when the partners of a successful start-up ask you to help to build a great agency, it's difficult to say no."
The creative team first paired up at Buckinghamshire College in the 90s. They launched their careers at Ogilvy & Mather, before moving to Miles Calcraft Briginshaw Duffy and then to AMV.
The pair were Campaign Faces to Watch in 2004 and have worked on ads including "fingerlegs" for the NHS and the Economist campaign.
Three weeks ago, Fallon lost another senior creative, when Micah Walker, the creative director on the agency's Orange account, left to join Publicis Mojo in Sydney.