Dempsey has been linked with Seattle Sounders but as yet there is no confirmation of which team he will play for.
The American international spent five years at Fulham, scoring over 50 goals, before moving across London to join Spurs in a £6m deal last summer.
He scored 12 goals in 43 appearances for the north London club last season but the arrival of Paulinho and winger Nacer Chadli this summer has left him surplus to requirements at White Hart Lane.
Dempsey, 30, made his name in the MLS with New England Revolution before Fulham brought him to the Premier League.
He is widely expected to sign with the Sounders, who are currently seventh in the Western Conference table.
Tottenham said in a statement: "We have reached agreement with Major League Soccer for the transfer of Clint Dempsey. We wish Clint every success for the future."