The 24-year-old winger made a total of just 11 first-team appearances for Spurs after initially joining the club on loan from Juventus in August 2011.
Falque featured in all three of Tottenham's preseason games during the club's tour of the United States this summer and scored a penalty in the club's 3-3 draw with Seattle Sounders, but has made the switch to Serie A.
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The 24-year-old winger initially joined White Hart Lane from Juventus on a season-long loan in August 2011 before his move was made permanent the following January.
Falque failed to appear in the Premier League during his time at Tottenham but featured 11 times in various Europa League, FA Cup and League Cup fixtures.
The Spaniard also spent time on loan at Southampton, Almeria and, most recently, Rayo Vallecano.
Falque is the fifth player to leave Tottenham this summer after Cameron Lancaster, Jake Livermore, Gylfi Sigurdsson and Heurelho Gomes.