Colombo worked for new Giants OC Jason Garrett in Dallas, so this should be a seamless fit for both sides.
New York had been connected to Bill Callahan in recent weeks, but he agreed to a deal with the Browns.
Colombo, 41, is a former first-round pick of the Bears back in 2002. He played 12 seasons in the NFL before taking his first coaching job with the Cowboys in 2016 as their assistant OL coach.
Dallas promoted Colombo to offensive line coach in 2018.