Neither player was available Saturday for the Knicks' 107-98 loss in Atlanta.
''We're going in a different direction and we've got to figure out another spot or two for our ballclub,'' coach Mike Woodson said before the game.
World Peace wrote on his Twitter account earlier Saturday that his agent was working on a buyout and thanked fans and the city.
Neither veteran has earned a place in Woodson's rotation in his first season in New York. Udrih has appeared in just 31 games, while World Peace, who had a procedure on his knee in January, has played in just 29.
''I can't say anything went wrong,'' Woodson said. ''Again, they weren't in the rotations. I'm not going to linger on it. I mean, we're buying them out. As a coach, guys work for me, I wish them nothing but the best as they move on and we're going to move on. So that's about the extent of it.''
Players have to be waived by March 1 if they hope to sign with another team and be eligible for the playoffs.
World Peace is a New York native who played at St. John's, and had long hoped for a homecoming. It didn't turn out to be a happy one with the Knicks, as his 7 minutes of playing time Friday in a double-overtime loss at Orlando was only the sixth game he'd gotten into in 2014.
All-Star Carmelo Anthony said he was surprised because World Peace seemed to be in good spirits a day earlier.
''He was happy, He played,'' Anthony said. ''On the bench, in the locker room, he was a different Metta. Maybe because he had the chance to get out there and play a little bit. But I wake up this morning and hear that he wanted a buyout, it took me by surprise.''
Udrih hasn't played since Jan. 24. There was speculation the point guard would be traded before Thursday's trade deadline.
''It's sad to see them go. But look, this is the business of basketball, man,'' Anthony said. ''For whatever reason, I don't know what's the reason that they wanted to get bought out. But it happened and we've got to move on from there.''
AP freelance writer Amy Jinkner-Lloyd in Atlanta contributed to this report.