Michael Cooper, who has been the interim coach, will return to his role as an assistant.
Karl is back in the NBA after an absence of less than two years. He previously coached the Cleveland Cavaliers, Golden State Warriors, Seattle SuperSonics and Milwaukee Bucks, and then worked as a TV basketball analyst.
"We are very excited to be adding a coach of George's stature to our organization," Vandeweghe said. "He has won everywhere he has been and his track record speaks for itself. We also want to commend Michael for the job he did under difficult circumstances."
The Nuggets are 17-25 this season. The team was 4-10 under Cooper, who took over in December after Jeff Bzdelik was fired.
Karl's NBA teams have had a combined record of 708-499.