Harrington was the Institute's co-director of cardiovascular research and the leader of cardiovascular trials.
The Institute, which was formed in 1969, is the largest academic clinical research organization.
Harrington succeeds Robert Califf, who is the director of the new Duke Translational Medicine Institute.
"Bob has played an instrumental role in making the Duke Clinical Research Institute what it is today and he is, without any doubt, the single most qualified individual to lead it in the next phase of its evolution," Califf said. "He is well-known, both nationally and internationally, as an inclusive leader who seeks collaboration as the primary method to advance the field."
Harrington has been part of the Duke faculty since 1993.