Nuggets President Josh Kroenke made the announcement, saying Shaw -- an assistant the past two seasons with the Indiana Pacers -- "brings a remarkable pedigree of success as both a championship player and a championship coach."
The Pacers, with Shaw as a member of the coaching staff, reached the 2013 Eastern Conference finals, where they lost to the eventual NBA champion Miami Heat.
Shaw, 47, was an assistant coach for seven years with the Los Angeles Lakers, who won two NBA titles during that time.
In a statement posted on the Nuggets' website, Shaw said Denver has "a talented roster with a great foundation."
"As a player and a coach, my primary goal has always been to win a championship," Shaw said. "I sincerely believe that Josh and Tim share that same vision."
Shaw, the 24th overall pick in the 1988 NBA Draft, played 14 season in the league for the Boston Celtics, the Heat, the Orlando Magic, the Golden State Warriors, the Philadelphia 76ers, the Portland Trail Blazers and the Lakers. He was with the Lakers when they won three consecutive NBA titles in 2000-02.