BOSTON — Kevin Garnett is leaving Minnesota after the Boston Celtics agreed to acquire the All-Star forward in a multiplayer trade with the Timberwolves, a Celtics official told the Associated Press yesterday.

Among the players who could be headed to Minnesota are forward Al Jefferson, guard Sebastian Telfair, swingman Gerald Green and center Theo Ratliff, said the official, who spoke on condition of anonymity because the deal had not been completed. The official also said the Timberwolves would get at least one draft choice.

The teams still had some things to clarify with the players’ contracts, but the official said that would not keep the Celtics from acquiring Garnett, although there could be a change in the players ticketed for the Timberwolves.

Garnett, 31, has spent all of his 12 NBA seasons with Minnesota. He would get an extension of his contract, which has one year plus an option year remaining, the official said. The Celtics had tried to get Garnett late last month, but his agent said he didn’t want to go to Boston.

Since then, Boston acquired seven-time All-Star guard Ray Allen from Seattle in a draft day deal. Already with Paul Pierce, the Celtics would become instant contenders in the mediocre Atlantic Division with Garnett, even without promising forward Jefferson.

The Celtics obtained Allen and the 35th pick of the draft for guards Delonte West and Wally Szczerbiak, and forward Jeff Green of Georgetown, whom they drafted with the fifth pick.

The Celtics have won just three playoff series during Pierce’s nine years with them. They still have an NBA-record 16 championships, but none since 1986.

“They have no excuses, this team out there,” Danny Ainge, the executive director of basketball operations, said after Allen was acquired.

Pierce, 29, led the Celtics in scoring last season but played only 47 games because of injury.

Allen, who turns 32 next month, averaged a career-high 26.4 points last season, his 11th, but underwent surgery to remove bone spurs on both ankles that required him to wear protective boots. He is expected to be ready for training camp. A long, lean 6-foot-11 forward who’s actually at least 2 inches taller than his listed height, Garnett’s athleticism has allowed him to play all over the court — banging against bodies in the post, swatting away shots in the lane, running the fast break, shooting top-of-the-key jumpers and even playing point guard every once in a while.

A preps-to-the-pros pioneer, Garnett’s immediate impact after being selected fifth overall in 1995 by the Timberwolves paved a path for dozens and dozens of other teenagers to skip college and declare for the draft – most of whom enjoyed far less success.

Then in October 1997, Garnett’s contract changed the game – a six-year, $126 million extension that led to significant alterations to the league’s collective bargaining agreement emerging from a 1999 lockout.