He’s got his team back.

“We’re the Eastern Conference champions,” Danny Ainge, general manager of the Boston Celtics, said Thursday. “And we think we’re going to be better next year.”

Ainge confirmed the Celts have agreements with Paul Pierce and Ray Allen that would keep Boston’s new Big Three intact for a run at a third NBA finals in four years. Ainge also said he expects to sign free-agent center Jermaine O’Neal to fill in as Kendrick Perkins recovers from knee surgery.

“We intend to sign him,” Ainge said. “Our priorities to start the offseason were obviously Paul and Ray, and to strengthen our center position in light of Perk’s injury. Hopefully by (today) we’ll have these things taken care of and we can continue working.”

Ainge said he thinks Boston remains the team to beat in the East, regardless of LeBron James heading to the Miami Heat, who already have agreed to terms with top free agents Chris Bosh and Dwyane Wade.

“I have a great deal of respect for all those guys, all the top-notch free agents,” Ainge said in Orlando, Fla., where the Celtics are playing in a summer league. “I know that it’s going to be a challenge. The East is going to be stronger. But I think everybody that’s worth their salt thinks they can beat somebody.”

Part of the reason for optimism could be that the Cavaliers, who had the best record in the NBA last season, would be diminished as a threat without James. And even with him, Cleveland lost to the Celtics in the playoffs in two of the past three seasons.

“There are a lot of franchises that are going to be changed for a long time,” Ainge said, “for the better and for the worse.”

And that’s why the Celtics are happy to make another run with the core of the team that won one title and came within four points of another, losing to the Los Angeles Lakers 83-79 in Game 7.

“How the team played in the playoffs is definitely a sign that they have a lot of basketball left in them,” Ainge said, noting that Perkins was injured in Game 6 and missed the finale. “I was very encouraged with what I saw from this team. The overall play of defense and rebounding showed me how much our guys do have left.”

Pierce agreed last week to a four-year deal worth about $61 million, and Allen agreed Wednesday to a two-year deal worth $20 million. O’Neal’s contract is reportedly for the midlevel exception, about $5.76 million in the first year of a two-year deal.

Kevin Garnett, the other member of the new Big Three that led the Celtics to their record 17th NBA title in 2008, is under contract for two more years, and Rajon Rondo is locked up through 2014-15. Coach Doc Rivers also put off a long-debated sabbatical to keep the team together.

“Paul, I don’t think he ever looked at another team. I think Paul was 100 percent coming back to Boston,” Ainge said. “He did a lot just by restructuring his contract to allow us to bring the rest of the team back.”

Ainge said Perkins could miss half the season or more. Surgery is scheduled for Monday, having been postponed at least twice to allow the swelling to go down and give him a chance to strengthen the muscles in his leg before the operation.

With Perkins on rehab, and backup Rasheed Wallace vowing to retire, the Celtics were in need of big men.

A six-time All-Star, O’Neal averaged 14 points and 7.5 rebounds in a 14-year career for Portland, Indiana, Toronto and Miami. With the Heat last year, he averaged 13.6 points and 6.9 rebounds in 28 minutes.

Remaining on Ainge’s list of potential free agents are re-signing longtime Celtics bench player Tony Allen and midseason acquisition Nate Robinson.

“We’re trying to fill our roster in. Once we get this taken care of the next couple of days, then we’ll start working on the next group of guys,” Ainge said. We like Nate and Tony. I’m sure they’re still looking at the market, too, because the market’s pretty crazy right now. So we’ll be patient and look at other options as well in case they go in another direction.”