"It was a tough decision. But it was one that I felt like needed to be done," the quarterback said in an interview with SiriusXM NFL Radio on Thursday.
He said Thursday his doctor told him his knee is "not gonna get any better, but it could get a lot worse."
The Jets signed Garrard in March as a potential alternative at quarterback to Mark Sanchez. The 35-year-old Garrard hadn't played in an NFL game the past two seasons because of back and knee injuries but was the starter with the Jacksonville Jaguars for several years before that. He passed a physical with the Jets this spring.
Garrard was the first major signing by new Jets general manager John Idzik.
Garrard said Thursday, the Jets' selection of Smith didn't factor into his decision.
"It didn't play into it at all. … It was really just my knee and my health," he said.
On a conference call with season-ticket holders earlier Wednesday, new offensive coordinator Marty Mornhinweg said the team's starting job is open.
"This will be a bona fide quarterback competition. Period," Mornhinweg said. "I'm hoping that somebody will rise to the top quicker rather than later."
With the departure of Garrard, it appears there are now two primary candidates: the struggling incumbent, Sanchez, and the former West Virginia star, Smith.
Garrard said Thursday that he believes the Jets are being truthful that the starting quarterback job is open.
"Honestly, they really said that it's an open competition. They're not leaning one way or another," he said.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.