NEW YORK — Relief. That was the look on Jason Giambi’s face all afternoon.

Wearing a bright-eyed smile stretched across his full cheeks, the New York Yankees star bounced around the field during batting practice Thursday and posed for photos with fans.

No wonder. He had plenty to be happy about.

Earlier in the day, commissioner Bud Selig announced he won’t punish Giambi because of the slugger’s charitable work and cooperation with baseball’s steroids investigator.

“It’s over and done with. I’m thrilled with it. He did what he needed to do — now I can go forward,” Giambi said before the Yankees lost to Detroit in the opener of an important four-game series. “I can go forward and not hurt the ballclub with a suspension.”

Selig, speaking on the second and final day of an owners meeting in Toronto, called this an “appropriate decision.”

Giambi has acknowledged a “personal history regarding steroids.” He agreed to speak with former Sen. George Mitchell last month after Selig threatened to discipline him if he refused to cooperate.

“He’s doing a lot of public-service work, and I think that’s terribly important,” Selig said. “I think it’s more important for us to keep getting the message out. He was, I thought, very frank and candid with Sen. Mitchell, at least that was the senator’s conclusion. Given everything, this is an appropriate decision.”

Giambi said he already was involved with most of the charity work in question “before any of this.”

“I felt they were good programs. They were great for kids,” he said.

Selig said June 21, before Giambi met Mitchell, that he would take “Giambi’s level of cooperation into account in determining appropriate further action.”

Selig said Mitchell was not expected to speak with any other active players.

“This was a special circumstance,” Selig said. “I have no other plans.”

No date has been announced for the release of Mitchell’s report.

Giambi met Mitchell in New York on July 13, becoming the first active player known to talk with baseball’s steroids investigator.

“Sen. Mitchell was great. We got along great. He knew I was in a tough situation and at the same time it was great the way he went about it,” Giambi said. “I’m just one piece of a huge puzzle.”

The 2000 AL MVP with Oakland, Giambi missed more than two months this season because of torn tissue in his left foot. He began the day batting .270 with nine home runs and 26 RBIs in 51 games.

Yankees general manager Brian Cashman didn’t have much reaction to Selig’s decision, saying the commissioner’s discretion about the health of the sport was more important than the club’s self-interest.

But manager Joe Torre was pleased with the news.

“The fact that it’s over and done with, it’s a little less he has to deal with. It’s closure. It’s something he treated with a great deal of respect,” Torre said. “The fact that he can just concentrate on baseball is good for all of us.”

Giambi started at first base Thursday night for the first time since returning from the foot injury. He went 1-for-5 with three strikeouts in an 8-5 loss to Detroit.

“Oh my God, it’s a miracle!” he said before the game. “Big G is loose today!”

On other matters:

—The commissioner’s office and the players’ association are discussing the possibility of starting the 2008 season in Tokyo, with the Boston Red Sox, Seattle Mariners and Oakland Athletics under consideration along with the Toronto Blue Jays and Los Angeles Dodgers.

—Selig said baseball does not intend to hold an official celebration to honor Barry Bonds for breaking Hank Aaron’s home run record. “I think my statement was appropriate and I don’t have any future plans,” he said. When Bonds broke the record, Selig issued a statement saying, “While the issues which have swirled around this record will continue to work themselves toward resolution, today is a day for congratulations on a truly remarkable achievement.” Asked whether he was happy with the way the record fell, Selig responded: “Look, it’s fine; it’s over, and I think I was.”

—On the Florida Marlins’ plans for a new ballpark, Selig said: “We need to make progress there. This team needs a new stadium. I’ve said many times I like South Florida. I think it’s a major league market. But it’s a major league market only if they get a new ballpark.”

—Selig said he hopes to decide on the host of the 2010 All-Star game in the next month or so. “Then I’ll determine 2011 and probably do a few of those. I’m going to try to go AL and NL alternating. I think that’s fair, since it does determine the home-field advantage (in the World Series).”