After graduating from the University of Colorado at Boulder in 2006, Copeland signed with the NBA D-League's Fort Worth Flyers on March 29, 2007. He then moved to Europe for the 2007–08 season. Over five seasons in Europe, he played for teams in Spain, the Netherlands, Germany and Belgium.
On July 16, 2012, Copeland signed a non-guaranteed contract with the New York Knicks. He made his NBA debut on November 2, against the Miami Heat. Copeland recorded a career-high 33 points against the Atlanta Hawks on April 17, 2013. Copeland won the Eastern Conference Rookie of the Month award in April. Copeland averaged over 8 points his rookie season.