The United States international returns to MLS after making 43 appearances and scoring 12 goals for Tottenham following his signing from Fulham last summer.
The north London side have also agreed a deal to sign striker Roberto Soldado from Valencia, which is likely to have restricted Dempsey's first-team chances.
The versatile midfielder, who has 99 caps for the United States, left New England Revolution in his homeland to join Fulham in January 2007.
He scored 50 goals in 184 league appearances for the Cottagers before Spurs beat Liverpool and Aston Villa to his signature last summer.
Goal revealed how Dempsey had grown frustrated with life at White Hart Lane and was hopeful of a move ahead of the 2014 World Cup in Brazil.