The team said it would provide an update on his rehab and progress around the start of training camp.
On Tuesday, Bullock signed a two-year, $8.2 million deal with the Knicks. The sides reworked the deal after his medical issue prompted the team to back out of its original two-year, $21 million agreement.
Bullock, 28, averaged 11.3 points in 63 games for the Detroit Pistons and Los Angeles Lakers last season. He was acquired by the Lakers ahead of the trade deadline in February in exchange for guard Sviatoslav Mykhailiuk and a second-round draft pick.
The procedure took place at the Hospital for Special Surgery in New York.