The deal was reported earlier this month during a signing moratorium, then held up while the Celtics tried to work out a sign-and-trade agreement with the Dallas Mavericks.
Instead, Boston will use its mid-level exemption to sign the 2009 NBA Sixth Man of the Year.
The 6-foot-2 guard averaged 15.1 points per game for the Mavericks last year. He was second in the league with 138 made 3-pointers last season and is fourth in NBA history on the career list with 1,788.
Terry is seen as a replacement for Ray Allen, who signed as a free agent with the Miami Heat.
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