Allen, 35, will provide depth on the wing, which is particularly important with Solomon Hill out for an extended period due to a hamstring injury.
Allen was named to the NBA second-team all-defensive team last season while playing for the Memphis Grizzlies. It was the sixth time in the past seven seasons he made an all-defensive team.
Allen averaged 9.1 points and 5.5 rebounds last season in 71 games, including 66 starts.
For his career, split between the Boston Celtics (2004-10) and the Grizzlies (2010-17), Allen has averaged 8.2 points and 3.6 rebounds in 798 games, 441 of them starts.