rasheed wallaceBOSTON — Rasheed Wallace is joining Boston’s Big Three as the Celtics hope the four-time All-Star will help them recapture the NBA championship.

Wallace, known for his shooting, rebounding and technical fouls, signed Wednesday, the first day free agents were allowed to do so.

One of the most coveted players available, Wallace joins Kevin Garnett, Paul Pierce and Ray Allen as the veteran corps of a team that lost to Orlando in seven games in the Eastern Conference semifinals one year after winning its 17th NBA title.

Terms of the reported two-year deal were not released. Wallace earned $13.68 million last season, his last of a five-year contract with Detroit.

The 6-foot-11 Wallace can play the low post and has exceptional shooting range. He averaged 12 points for the Pistons last year, the 14th straight season in which he’s scored at least 10 per game.

Celtics general manager Danny Ainge said the team was “ecstatic” to add a player with Wallace’s talent and championship experience. He won a title with Detroit in 2004.

Wallace, a starter his entire career, figures to back up Garnett at power forward and Kendrick Perkins at center. Garnett is expected to be at full strength when the season starts after he had postseason knee surgery.

The Celtics also could retain Glen Davis, a restricted free agent who filled in well when Garnett was sidelined for the playoffs. They have the right to match any offer from another team.

Wallace has averaged 15 points and 6.9 rebounds with 1.4 blocks while playing almost 34 minutes per game in his 14 seasons. Now he must adjust to a backup role after starting 943 of his 1,009 regular-season games.

He also must try to keep his temper in check.

His 41 technical fouls in 2000-01 while with Portland still stands as the NBA’s single-season record. During the 2008 playoffs, the league fined him $25,000 for his expletive-laced criticism of officials Mike Callahan and Kenny Mauer after the Celtics won Game 5 of the Eastern Conferences in Boston.

“The cats are flopping all over the floor and they’re calling that,” Wallace said then. “That ain’t basketball out there. It’s all entertainment. You all should know that.”

The Celtics captured the series by winning the next game then beat the Los Angeles Lakers in six games for the NBA title.

Last season, Wallace was suspended for Detroit’s game at New Jersey on April 1 after picking up his 16th technical of the season the previous night. Each foul after the 15th in a season carries an automatic suspension.

But Ainge loves Wallace’s rebounding, defense and ability to draw big men from the basket with his 3-point shot.

“We are ecstatic to be able to add a player the caliber of Rasheed Wallace to our team,” Ainge said. “It is not everyday that you can add a four-time All-Star and a player with championship experience.”

The Celtics put a full-court press on Wallace in their bid to bring him to Boston. Last week, Ainge, coach Doc Rivers, owner Wyc Grousbeck, Garnett, Pierce and Allen visited him at his home in the Detroit area. His agent, Bill Strickland, said during the weekend that Wallace had decided to join the Celtics.

With all four veterans in their 30s, the Celtics could be entering their last few years of contending for a title.

When the season starts, Wallace will be 35, Allen 34, Garnett 33 and Pierce 32. But Ainge said last week that the Big Three could play with Boston beyond their current contracts.

Allen has one year left on his deal, Pierce has two and Garnett has three.

“If they take good care of themselves, which all three of them do, and they stay healthy I think there’s a really good chance,” Ainge said. “I think all those guys will be up in my office pretty quick looking for more years on their contracts.”

With Wallace signed, Ainge has more time to work on an extension for point guard Rajon Rondo, who can become a free agent after the coming season.