Logan is available to pitch when the Rockies face the Chicago White Sox on Monday night.
Logan was placed on the disabled list March 21 with inflammation in his left elbow. He allowed one run and three hits in two-thirds of an inning in his only appearance in spring training.
Logan signed a three-year contract with Colorado last winter after four years with the Yankees.
Dickerson made Colorado's opening-day roster this year after hitting .344 in spring training. He is hitting .200 in five plate appearances in 2014.
The Rockies have a full 40-man roster.