The team announced the deal Tuesday. Financial terms of the agreement weren't disclosed.
"Trey's experience as a ballhandler matched with his scoring ability makes him a good fit for our roster," 76ers general manager Elton Brand said in a statement. "We're excited to welcome him to the 76ers and look forward to the positive impact he can have on our team."
Burke appeared in 58 games last season with the Knicks and Mavericks. He averaged 10.9 points, 2.7 assists and 1.7 rebounds in 19.4 minutes per game.
For his career, Burke has played in 361 games (128 starts) over six seasons with the Washington Wizards, Jazz, Knicks and Mavericks. He has averaged at least 10 points per game in five of his six NBA seasons.
"Excited to be here. Excited to get to work and get started," Burke said. "Let's go get this championship. Go Sixers."