The Knicks had until Friday to pick up the option or pay Billups a $3.7 million buyout.
"Chauncey, Amare [Stoudemire] and Chauncey [Billups] are a great nucleus, as we continue to look to improve our team going into the offseason," Knicks president of basketball operations Donnie Walsh said in a statement. "Chauncey is an extremely talented and experienced point guard -- we are very happy to have him back."
The 13-year veteran missed three of the Knicks' four playoff games, all losses, to the Boston Celtics after straining a knee tendon late in Game 1 of their Eastern Conference first-round series.
The Knicks had no immediate word on Walsh, who also has a team option on the fourth year of his contract, which expires June 30. There have been reports the Knicks are considering offering Walsh a two-year extension. He was expected to meet with Madison Square Garden chairman James Dolan this week.
Billups will be 35 in September and said this week he hoped to return to New York for his 15th NBA season. After playing most of his career at 215 pounds, Billups said Monday he planned to come in at 210 next season to better handle the pace of Mike D'Antoni's system. He insists he has plenty of basketball left.
"My body has been great," Billups said. "I'm 34, not 39. My first five years I didn't play that much anyway, unfortunately, but my body is fine."
There wouldn't be many point guard options this summer better than Billups, a former NBA Finals MVP who is a top late-game performer. He didn't take long to prove it in New York, hitting a go-ahead 3-pointer with 1:01 left in a win at Miami on Feb. 27, just four days after his Knicks debut.
But the sweep by Boston was an unusually early exit for the five-time All-Star, who reached the conference finals seven straight years with Detroit and Denver from 2003 to 2009, and said he wanted to be around when the Knicks brought championship-caliber basketball back to New York.
"Getting swept in the first round, I don't do this," Billups said. "This is not fine with me, so I like to play later in the season, I want an opportunity."
Chris Sheridan covers the NBA for ESPN.com. Information from The Associated Press was used in this report.