Meyer was suffering from chest pains and self-medicating for his stress.
"Now I'm taking two Ambiens," Meyer told the HBO show. "I would drink a beer on top of it, just to get some sleep. Not many people know that.
"And I go from 217 pounds to 180 pounds. I lose 37 pounds."
That all occurred when the Gators were undefeated in 2009 -- until losing to Alabama in the SEC title game.
After the loss to the Crimson Tide, Meyer was admitted into a hospital with chest pains.
"They said, 'We don't believe it was a heart attack.' " Meyer said. "So, OK, 'Well, what is it?' 'We don't know.'
"And then you start thinking, 'There's something wrong with me mentally, you know? What is going on here?' "
Meyer said he was depressed.
"I thought I was dying," Meyer said. "Mentally, I was broke."
Meyer said after Florida won the national title after the 2008 season he didn't -- and couldn't -- enjoy the victory. He began recruiting literally minutes after the 24-14 win over Oklahoma in the BCS title game in Miami ended.
"I was in a panic situation," Meyer said. "We just won it. We got to do it again. I close the door. And I started just recruiting. One of my friends came and said, 'What are you doing?' He said, 'Enjoy, what's wrong with you, man? Enjoy this.' I tried."
In 2009, Meyer resigned as Florida's coach before the Sugar Bowl, but then changed his mind and stayed. He left Florida for good after the 2010 season. He worked as an ESPN analyst in 2011 before becoming Ohio State's head coach in 2012.
The "Real Sports" episode featuring Meyer debuts Tuesday at 10 p.m. ET.