The deal came shortly before the NBA trade deadline and was the feature transaction of a busy day.
Boston's trade with Oklahoma City centered around Perkins and Green, both of whom have played a key role for their former teams.
Green, a forward, has averaged 15.2 points and 5.6 rebounds in 49 games this season. Perkins recently returned from knee surgery and played in only 12 games for the Celtics. His inside presence was a key factor in Boston winning the league title two seasons ago and his knee injury during last year's playoffs perhaps cost the Celtics another championship.
Krstic has started 47 games at center for the Thunder this season and has averaged 10 points and five rebounds per contest in seven seasons with New Jersey and Oklahoma City.
Robinson has come off the bench at the guard position for most of the year with averages of 7.1 points and 1.9 assists.
Perkins will give Oklahoma City an additional element of inside strength to go with the play-making abilities of Kevin Durant and Russell Westbrook.
The Celtics were involved in three trade-deadline deals Thursday and all that action left Boston shorthanded when it played in Denver.
"We have eight guys and we're going to try to win the game," Boston Coach Doc Rivers said. "We'll have to figure it out tonight."
In other deals Thursday:
-- Cleveland acquired center Semih Erden and forward Luke Harangody from Boston for a second-round pick in the 2013 draft.
-- Portland received all-star forward Gerald Wallace from Charlotte in exchange for center Joel Przybilla, forward Dante Cunningham, forward/center Sean Marks and two future first-round picks.
-- Boston dealt forward-guard Marquis Daniels to Sacramento for a protected second-round pick in the 2017 draft.
-- Houston traded forward Shane Battier and guard Ishmael Smith to Memphis for center Hasheem Thabeet, forward DeMarre Carroll and a first-round draft pick.