Offensive coordinator Steve Addazio will serve as the Gators' interim coach in his absence, but Meyer, 45, will coach No. 5 Florida against Cincinnati in the Sugar Bowl on New Year's Day.
"It's full speed ahead. We're going to do everything possible we can do to win this game," he said.
Meyer also said he expects to be back on the Florida sideline at the start of next season.
"I do believe in my gut that will happen," he said at a news conference in New Orleans.
He told reporters he was offered and encouraged to take a leave of absence earlier in the week. He said being with his players at a "spirited practice" Sunday morning persuaded him not to resign.
"I want to do right by my family, and my second family are my players and our staff," he said.
Meyer stunned the college football world Saturday when he announced he would leave Florida after five seasons because of concerns for his health.
The Florida coach was rushed to a Gainesville hospital Dec. 6 after suffering major chest pains. He said Sunday that he had actually experienced chest pains for the past four years, and that they had become "rather significant" two years ago.
The Dec. 6 scare made him re-evaluate his priorities, and he decided this past weekend that he would step down.
"I was advised that I would have to get this right or it would lead to damage," he said.
Asked by reporters what changed his mind about resigning, Meyer said, "It's very simple -- the love that I have for my players."
Florida athletic director Jeremy Foley said keeping Meyer healthy would remain paramount.
"Obviously our primary concern here us Coach Meyer and his health and getting himself fixed," Foley said. "And he's going to have the opportunity to do that."
Rivals.com site GatorBait.net cited multiple sources as saying Meyer talked to the players Sunday as their plane sat on the tarmac in Gainesville before their flight to New Orleans. On the plane, Meyer floated the idea that he might return.
Word spread quickly after that. Several recruits heard the news and sought more info.
Lineman Leon Orr, from Gulf High in New Port Richey, Fla., called Gators defensive line coach Dan McCarney, who confirmed that Meyer had changed his mind.
"I'm real excited," Orr said. "I'm glad he's just taking a leave of absence."
Meyer is 56-10 as the Gators' head coach, including 32-8 in the SEC and a school-record 22-game winning streak that ended against Alabama in the SEC title game on Dec. 5.
Meyer came to Florida from Utah in fall 2004 amid speculation he would end up at Notre Dame. He brought most of his staff with him -- some of whom worked with him at Bowling Green (2001-02) and Utah (2003-04).
Two years later, Florida won its second national championship by upsetting Ohio State 41-14 in Glendale, Ariz.. The Gators won another one last January by beating Oklahoma 24-14 in Miami.
Meyer is married with three children and has said repeatedly he planned to leave coaching to spend more time with his family.