It continued: "The Galaxy MVP in 2012, Keane led the team with 16 goals in 28 regular-season games while adding nine assists. In the post-season, Keane led MLS in goals with six as he led the Galaxy to their second consecutive MLS Cup championship.
"Per club and league policy, details of the contract were not released."
Keane has scored 18 goals in 32 regular-season games since arriving in America, adding seven goals in 10 post-season games.
He was named in the MLS Best XI for the first time in 2012.
Keane is training with Spurs for the next two weeks in a bid to maintain his fitness ahead of the start of the new MLS season in March.
Meanwhile, the Galaxy announced that Brazilian midfielder Juninho had also penned a multi-year contract, having spent the past three seasons with the club on loan from Sao Paulo.