Financial terms were not announced but Allen will be in the second year of a two-year $20 million contract he signed last summer, Boston media reported.
His decision will keep three of the Celtics' top players, Allen, Kevin Garnett and Paul Pierce, together for another year.
Allen averaged 16.5 points in helping the Celtics to the Eastern Conference semi-finals during the 2010-11 season. They were eliminated by the Miami Heat.
He became the NBA's all-time three-point field goals made leader in February and ranks 24th among NBA career scorers.
(Reporting by Gene Cherry in Raleigh; Editing by Julian Linden)