The Nuggets also get cash in the deal announced by Mark Warkentien, Denver's vice president of basketball operations.
The Knicks are expected to waive Green and Jones at a savings of about $2 million. Both players have non-guaranteed contracts.
A former first-round pick, Balkman was going to struggle to find minutes in a crowded forward rotation. The Knicks took another forward, Danilo Gallinari, with the No. 6 selection in the June draft.
"Renaldo really had no role after we drafted Gallinari, and with the emergence of Wilson Chandler his minutes would be nonexistent," Knicks coach Mike D'Antoni said in Macau, where is on the U.S. Olympic team staff. "So it really wasn't fair to him to keep him in a spot that he wouldn't play and also gives us an opportunity to clear up a roster spot and move on."
The 6-foot-8 Balkman averaged 3.4 points and 3.3 rebounds in 65 games for the Knicks last season. He has averaged 4.2 points and 3.8 rebounds in two seasons with the Knicks, shooting .499 from the field.
Green averaged 1.1 points in nine appearances with Denver last season. Jones averaged 3.4 points and 1.5 rebounds in two stints with the Nuggets during the 2007-08 season.
Information from The Associated Press was used in this report.