The club said on its Twitter site that he "returned from the hospital and will be travelling with the team back to Pittsburgh."
During the game, the Penguins said on their site that he was taken to Massachusetts General Hospital where "he is alert and conscious."
It happened in a wild sequence of events. Boston's Brad Marchand was injured on the other end when Thornton came skating up quickly from centre ice and grabbed Orpik from behind, knocking him down backward before punching him.
Thornton, dressed in a suit and speaking very quietly in front of his locker after the game, said he was "sorry" for what happened.
"It's hard for me to talk about right now. I can't say I'm sorry enough. I'm sure I'll be criticized, but it's true," he said. "I felt awful. It wasn't my intention. I know Brooksie. I've gotten to know him the last seven years here. I skated with him during the lockout. I texted him a couple of times. It's not what I wanted to see or anyone to see."
In TV replays, it appeared that Orpik didn't move after taking the punch. He also appeared hit his head on the ice when he fell. Thornton was given a match penalty.
Thornton has a hearing with the NHL.
"I hope he's doing all right," Thornton. "I heard he's conscious and talking and I'm happy about that."
Penguins coach Dan Bylsma said Orpik has a concussion.
"I think he was out on the ice for a period of time," Bylsma said. "So I think that means he's got a concussion, for sure."
Players immediately called for medical assistance for Orpik. He was surrounded by members of both team's medical staffs before he was taken off on a stretcher after about a 10-minute delay.
Pittsburgh's James Neal was assessed a kneeing penalty for his hit on Marchand.
"I mean, what do you want me to say? That I was trying to hit him?" Neal said. "No, I'm going by him. I don't get out of the way, like I said. I need to be more careful and I guess get my knee out of the way, but I'm not trying to hit him in the head or injure him or anything like that."
In the game's opening minute, Orpik hit Boston's Loui Eriksson with his shoulder near the winger's head as he turned to move up the ice.
"I think that's a big reason why," Penguins captain Sidney Crosby said when asked why Thornton may have reacted like he did.
Eriksson was stunned and went to the bench dazed before heading to the dressing room with a trainer taking one arm to help his balance as he got up from the bench.
Eriksson didn't return to the game.
Bruins coach Claude Julien said Eriksson left with a concussion and will not travel to Toronto for Sunday's game.
A few seconds after Orpik's hit on Eriksson, Boston captain Zdeno Chara charged at the defenceman and drew a cross-checking penalty.
Boston forward Milan Lucic also fought the Penguins' Deryk Engelland midway into the period.