Kitchens' hiring is a move that has been in the works for several weeks, ever since he was fired after a 6-10 season and the Giants named Joe Judge their head coach. In 2004 and '05, Judge and Kitchens were together at Mississippi State, where Judge was first a player and then a graduate assistant.
Kitchens was the Bulldogs' tight ends coach in 2004.
"Ultimately, you want to work with guys you have relationships with, professionally and personally," Judge said last week. "You know what to expect."
The news of Kitchens joining the Giants was first reported by Fox Sports.
Kitchens is the latest addition to the staff to have head-coaching experience. This could prove valuable considering Judge has never been a head coach at any level.
Offensive coordinator Jason Garrett and Kitchens have been head coaches in the NFL. Garrett had a nine-year stint with the Dallas Cowboys that ended after this season. Kitchens spent one turbulent season in charge of the Browns but has a long history of working with tight ends. He coached tight ends at Mississippi State and for the Cowboys (2006) and the Arizona Cardinals (2007-12).
Outside linebackers coach Bret Bielema and offensive assistant Derek Dooley have also been head coaches, at the college level; Bielema at Wisconsin and Arkansas and Dooley at Louisiana Tech and Tennessee.
Kitchens, who originally came to Cleveland as a running backs coach, took over as offensive coordinator midway through the 2018 season after head coach Hue Jackson was fired. With Kitchens calling plays, quarterback Baker Mayfield thrived and went on to break the NFL rookie record with 27 touchdown passes.
The offensive surge in the second half, propelling the Browns to a 7-8-1 finish, prompted former Browns general manager John Dorsey to make Kitchens his first head-coaching hire in Cleveland, even though Kitchens had never been a head coach at any level. Although the Browns hadn't won their division in 30 years, expectations for Cleveland ballooned even higher when Dorsey traded for All-Pro wide receiver Odell Beckham Jr. from the Giants in the spring.
But with Kitchens still calling plays, the offense never found a groove. Mayfield threw 21 interceptions, the offensive line struggled to protect him, and star wideouts Beckham and Jarvis Landry battled nagging hip injuries.
Cleveland ranked just 22nd in offensive efficiency and scored more than 30 points only twice all season. Meanwhile, without suspended star edge rusher Myles Garrett, the Browns' defense crumbled down the stretch, surrendering at least 30 points in each of the final three games.
After a loss to the Cincinnati Bengals to close out the year, Kitchens admitted this season failed to meet expectations.
"Six and 10 is not even remotely good enough," he said. "We're not running an operation here to try to be 6-10."
ESPN's Jake Trotter contributed to this report.