The 29-year-old helped United win the Championship title in 2019/20 and now links up with Stevie Crawford's squad at East End Park.
Watson was with Ipswich Town as a youngster and played for Livingston, Raith Rovers and Falkirk before a switch to Tannadice two years ago.
Dunfermline have also signed full-back Steven Whittaker from Hibernian, with the Scotland internationalist taking up a player/coach role.
