By Gary Washburn, Globe Staff

The Celtics continue to shore up their roster for another title run in 2012-13 by agreeing to a three-year contract with former Dallas sharpshooter and Sixth Man of the Year Jason Terry for the full mid-level exception of $5 million.

Terry, 34, was offered a two-year deal for more money to return to the Mavericks but decided on the extra year. Terry is the off-the-bench scorer the Celtics have been seeking, averaging 15.1 points in just 31.7 minutes per game as a reserve last season. After starting most of his first eight seasons, Terry became one of the league's top bench players, burning teams with his long-range shooting.

The Celtics remain interested in Ray Allen, who while the all-time leading 3-pointer shooter, was never comfortable with scoring in volume off the bench. Terry likely would fill a different role than Allen if Allen is retained.

Terry agreed to the deal while at an AAU basketball tournament in Orlando, Fla., where his daughters were participating.The 10th overall pick in the 1999 draft, Terry spent his first five seasons with the Atlanta Hawks before being traded to the Mavericks in Aug. 2004 in a deal that included former Celtic Antoine Walker.

Terry is fourth in league history with 1,788 3-pointers, trailing only Allen, Reggie Miller and former teammate Jason Kidd.