The agency saw off competition from Abbott Mead Vickers BBDO in a final shootout to clinch the business, worth around £1 million.
Tate will work with Fallon's communications planning arm, Happen at Fallon, which was recently launched as a joint venture with Naked Communications.
The venture aims to develop ideas beyond traditional advertising.
Tate's four UK galleries, Tate Britain, Tate Modern, Tate Liverpool and Tate St Ives, receive around six million visitors a year.
Phil Dowgierd, the head of Happen at Fallon, said: "Tate is the national and global benchmark within its sector."
TBWA held the Tate Britain account between 1997 and 2000. After that the business was handled by Miles Calcraft Briginshaw Duffy.