Karl, 53, is expected to make his debut tonight at Milwaukee against the team that fired him in 2003. Interim coach Michael Cooper will stay on as an assistant.
"He's clearly one of the best coaches in the NBA, has always been so, and his record exhibits that," Nugget General Manager Kiki Vandeweghe said. "We are very excited to have him."
Jeff Bzdelik was fired Dec. 28 after a 13-15 start. The Nuggets then were 4-10 under Cooper.
Denver (17-25) has disappointed after earning the final Western Conference playoff berth last season. Karl, however, said the playoffs are a realistic goal for a team expected to improve from last season after adding Kenyon Martin to a squad that featured Carmelo Anthony.
Karl also has set his sights on Anthony.
"I'm going to be demanding of certain things that he might not be happy with, but I also respect that he's a great talent," Karl said. "[His] being successful will only make my job successful. I'm just going to communicate with him, coach him, mentor him, try to teach him professionalism. I see a great player that has plateaued."
Karl is 708-499 in 16 seasons and took Seattle to the NBA Finals in 1996. He led the SuperSonics to at least 60 wins three times in five years and has made the playoffs in 13 of his 16 seasons.
Karl was an analyst for ESPN after the Bucks fired him in 2003, and his NBA coaching career also includes stops in Golden State and Cleveland.
Though tests revealed no further damage to his sprained left ankle, Cleveland Cavalier guard LeBron James' status is doubtful tonight at New York, the team said.
New Orleans Hornet guard Baron Davis will be sidelined at least another week because of a bruised right ankle, the team said. Davis has sat out five games since being kicked in the ankle Jan. 16 against Toronto.
Detroit Piston center Ben Wallace's brother David, who did not appear along with nine others at Tuesday's hearing involving the Nov. 19 brawl, appeared in court in Rochester Hills, Mich., pleaded not guilty and was released on $500 bond on a misdemeanor assault and battery charge.