The trade had been widely reported a few days ago, but did not become official until Monday.
Gay, 29, is the key component of the trade. He averaged 19.4 points and 7.4 rebounds this season for Toronto in 18 games, all as a starter.
Vasquez is the Raptors most important addition from the trade. He started all 18 games this season for the Kings, and averaged 9.8 points and 5.3 assists.
The Memphis Grizzlies have announced that guard/forward Quincy Pondexter is out indefinitely with a fractured right foot.
An MRI revealed that Pondexter has a tarsal navicular stress fracture in the foot.
Minnesota Timberwolves forward Corey Brewer has been fined $5,000 by the NBA for violating the league's anti-flopping rules for the second time this season.
The incident occurred with 2:51 left in the first quarter of Saturday's 103-82 loss to the visiting Miami Heat.
The Toronto Raptors have waived guard D.J. Augustin.
Augustin, 26, was signed as a free agent in July, but appeared in only 10 games for the Raptors this season, averaging 2.1 points, 1.0 assists and 8.2 minutes.
The Cleveland Cavaliers have recalled guard/forward Carrick Felix and center Henry Sims from the Canton Charge of the NBA Development League.