While the team did not disclose the terms, O'Neal is inked for two seasons and will receive the full midlevel exception of about $5.76 million this year.
"When the opportunity arose for me to join an organization like the Celtics, I could not refuse," said the 6-foot-11, 255-pound center. "I cannot wait to get to Boston and start to practice with the rest of the team in pursuit of a championship."
O'Neal says he's hungry for a ring and knows the Big Three and the remaining core from the 2008 title team are hungry for another, so that's why he chose Boston over other suitors.
"We're very excited to have him here," said Celtics president of basketball operations Danny Ainge. "He brings a great deal of leadership and knowledge."
O'Neal started all 70 games he played for the Miami Heat in 2009-10, averaging 13.6 points and 6.9 rebounds in 28 minutes per game. O'Neal has averaged 14 points and 7.5 rebounds in a 14-year career for Portland, Indiana, Toronto and Miami. He decided it was time to take his talents and depart South Beach.
"I knew what [the Heat] were trying to do, and I could have re-signed back with those guys," he said Wednesday after passing his physical with the Celtics. "But it comes down to fit. It comes down to personalities and style of play, and I thought Boston has all that for me. It came down to winning now, and not worrying about chemistry."
For now, he is expected to start in place of injured center Kendrick Perkins, and after that he is content to fill a role off the bench for a team that won it all in 2008 and returned to the NBA Finals this year.
"Being a part of something great is what matters to me," O'Neal told reporters at the team's workout facility. "I know what the city represents. I know what the organization represents. I know what the guys on the court represent. Obviously, those guys they have a ring already, but they want another one. I don't have one, and I want one. They know what it takes to get one."
Perkins went down in Game 6 of the Finals against the Los Angeles Lakers and missed the decisive game. He had reconstructive surgery on his right knee Monday, and he is expected to be out until at least February.
That left the Celtics in need of a big man, and O'Neal will only partially fill the role.
"When he comes back, it's his position to have," O'Neal said. "I'm just here to do my job. I'm not trying to step on anybody's feet. I'm not trying to do anything to cause any issues. I'm here to win. That's just really what it boils down to.
"I probably wouldn't have wanted to back up anybody. But this situation is proven, and why come in and try to mess up something that's already proven?"
Ainge said he wasn't done shopping for big men, but he said he didn't expect Rasheed Wallace to change his mind about retiring.
Still, O'Neal was doing his best.
"He had a lot of great things to say about the organization," O'Neal said. "That was kind of the selling point too -- [Wallace] coming in and him actually being here for a year and understanding the situation, the scenario, the chemistry.
"I shot him a text and I told him to come back. He didn't respond."
A six-time All-Star, O'Neal acknowledged that he is in "the stretch run" of his career but he denied that his skills had diminished to the point where he could no longer contribute.
"I believe that my play will speak for itself," he said.
He mentioned that he has played in the conference finals, made the Olympic team -- an injury kept him from playing in the Athens Games -- and been the focus of a shoemaker's marketing campaign.
"I'm not at a point in my career where I need to worry about that," he said. "I could play five more years. But hopefully I could win it next year, and then win it the next year and then walk away."
Ainge will try to talk him out of it.
"We think he's a perfect fit and complement to the players we have on the roster right now," the GM said. "Maybe for much longer than the next couple of years, but for the next couple of years, for sure."
O'Neal did not play in seven of the last 12 regular-season games, but he returned for the first-round playoff series against Boston. He totaled 21 points in the five games, making just 20 percent of his shots.
O'Neal said he got kicked in the left ankle with three games left in the regular season but played in the playoffs despite being injured.
"To me, when you suit up and you go out there, you're telling your team and your followers that you're ready to play," he said. "Whatever excuses you have should be kept in the locker room. So I chose not to talk about it, because it didn't really matter. I still felt like I could go out there and help the team, and unfortunately, I couldn't do it."
Ainge said the sprained ankle showed up during O'Neal's physical on Wednesday.
"He had a little bit of a sprain and that showed up in the testing," Ainge said. "We checked him out thoroughly. We're not concerned about him, except in the way we're concerned about any player."
Chris Forsberg covers the Celtics for ESPNBoston.com. Follow him on Twitter. Information from The Associated Press was used in this report.