Francis arrived on a flight from Rome at Bogota's military air base.
He was greeted by President Juan Manuel Santos and Colombia's national symphonic orchestra playing classics by Vivaldi and Beethoven as well as traditional music.
The visit has been a few years in the making but was delayed as the Colombian government's negotiations with the Revolutionary Armed Forces of Colombia stretched on.
Francis was a big promoter of last year's peace deal with the rebel group but in visiting Colombia he will have to be sensitive to the viewpoints of the large number of conservative Roman Catholics who voted against the accord in a nationwide referendum.
