Directors of the Colombian Football Federation had already held a meeting with the Portuguese during the Libertadores final match between River Plate and Boca Juniors in early December.
Now, the two parties have reached agreement, directvsports.com reported.
Jose Pekerman left his role as coach of Colombia after the 2018 World Cup, where the Cafeteros lost to England on penalties in the round of 16, and has since been under the guidance of under-20 boss Arturo Reyes on an interim basis.
Queiroz’s contract will run until the 2019 AFC Asian Cup.