The council voted 7-2 on Tuesday after a lengthy meeting. The effort was championed by Mayor Kevin Johnson, a former three-time NBA All-Star.
The city had nearly lost the team to Seattle last year, a fight that resulted in new ownership and a deadline to replace the Kings' aging home.
Under the deal, the city would be responsible for a $223 million subsidy, much of it financed through a parking revenue bond. The Kings would contribute $254 million to construct the arena and develop surrounding land.
Construction on the crown-shaped sports facility will break ground this summer and open in time for the 2016-17 season.