The Cowboys are flying to New York a day early to visit the site of the World Trade Center on Friday.
Garrett was inspired after he and his wife, Brill, went to the site of the Sept. 11, 2001, attacks last summer.
"I probably wasn't there for 10 minutes and I kind of looked around and said, 'We've got to somehow, some way get our football team here,'" Garrett said Tuesday, via the Dallas Morning News.
Garrett was a backup quarterback with the Giants and was living on the Upper West Side of Manhattan when the attacks happened. He was among the Giants players who went to the site in the days after to pass out water and greet first responders.
In the past during training camp, Garrett has taken the Cowboys on visits to the Navy SEALs and Marine Corps at their California bases.
Garrett said the Cowboys will hold a team dinner at One World Trade Center.
"I think it'll be a good experience for everybody," Garrett said. "It'll be great to expose our team, particularly because of their age. A lot of them were young when this happened. So I think the exposure to it -- the tragedy of what it was and then the response from everybody in that area and all across our country -- I think it's significant to our country's history and inspirational to everybody. I think it'll be a really special evening to our team."
Cowboys owner Jerry Jones mentioned the team's early departure during his weekly radio show on 105.3 The Fan in Dallas.
"Jason is really into those kinds of things for the team," Jones said. "We're going to go to Ground Zero and go to the observation tower and really experience that in the downtown area of New York and get a feel for what really heroes were like during those trying times."