The Boston Herald, citing a league source, first reported last week that the deal is for two years and will pay around $4 million per season.
The diminutive backup came to Boston at last year's trading deadline and provided a burst of energy off the bench in the playoffs. Celtics general manager Danny Ainge says Robinson might be able to help more after going through a full training camp and season.
Robinson shot 41.4 percent from 3-point range for the Celtics last year.
Despite measuring only 5-foot-9, Robinson is the only three-time winner of the NBA's slam dunk contest.
Information from The Associated Press was used in this report.