The Padres and White Sox had reached an agreement, but needed the 2007 Cy Young Award winner to waive his no-trade clause.
"As of right now, this is the best place for us to be. We made that decision for the time being," Peavy said before Thursday night's game against San Francisco.
"It's been a crazy 24 hours," he said. "I don't want to be any kind of distraction to the team. We're playing as well as we possibly can, winning five in a row and I've got a big game tomorrow night vs. the Chicago Cubs."
Peavy said he would answer additional questions about his decision after Friday night's start.
White Sox general manager Ken Williams said in a statement the organization still has "championship aspirations for this season" and will keep looking to improve.
Several hours before Peavy spoke, his agent, Barry Axelrod, said "my suspicion is he still has a strong preference to stay in the National League."
"There was a question posed to us as to whether Jake's position on going to the American League was still cast in stone or whether he'd consent to going to an AL team, specifically, the White Sox," Axelrod said.
Peavy, who turns 28 later this month, is 3-5 with a 3.82 ERA. He made his major league debut with San Diego in 2002.
Peavy and his wife have three sons, all under the age of 8.
"I understand where Jake is coming from given the unusually early timing of this type of event," Williams said. "It's understandable that he was caught a bit off guard, as most people in his position would be. He has a wife and three young boys to consider, and Jake has earned the right to thoroughly think through this move."
The Padres talked to the Cubs and Atlanta Braves during the offseason about a deal for the pitcher.
Several reports said the White Sox would've sent top pitching prospect Aaron Poreda and young left-hander Clayton Richard to San Diego as part of the package for Peavy.
While they were waiting for Peavy's decision, the White Sox lost 20-1 to the Minnesota Twins.
"I hope he don't watch the scoreboard because he might say no," White Sox manager Ozzie Guillen said.
Outside the players' garage at Petco Park in San Diego, someone hung a sign on a lamp post that read: "5/21/09, the day Padre baseball died. Don't take the trade Jake."
Peavy didn't, and will stick around. For a while, anyway.
Peavy made his announcement in the Padres dugout. Sitting next to him was 14-year-old Rory Wagner, a thyroid cancer patient who had wanted to spend time with Peavy and play catch with him.
San Diego did complete one trade Thursday, getting outfielder Tony Gwynn Jr. from Milwaukee for outfielder Jody Gerut. Peavy hugged Gerut before he left for the Brewers.
The Padres, who lost 99 games last season and aren't expected to contend this year, have been cutting payroll. Peavy is to earn $11 million this season, $15 million in 2010, $16 million in 2011 and $17 million in 2012. The Padres have a $22 million option for 2013 with a $4 million buyout.
Padres general manager Kevin Towers said Peavy is aware of the situation.
"He's a very mature young man, Towers said. "He understands what's happening. I think he will handle it well."
White Sox chairman Jerry Reinsdorf has expressed concern about spending big money in the current economic climate. Several older, high-paid players -- including Jim Thome, Jermaine Dye, Jose Contreras and Octavio Dotel -- can leave after this season, and that would've freed up payroll for the most expensive part of Peavy's contract.
The White Sox are off to a slow start, but are expected to contend in the closely bunched AL Central.
"Having him in the rotation would be great," Guillen said earlier in the day. "He's one of the best in the game -- if not the best in the game, at least the National League. He's going to make our ballclub a lot better."
Had he accepted the trade, Peavy would have anchored a strong rotation along with Mark Buehrle. Instead, he's scheduled to take the mound Friday against the Cubs.