Cheney, 71, was recovering in the Intensive Care Unit of Inova Fairfax Hospital in Falls Church, Va. His office would only say he is recovering but did not discuss his condition.
The aide said Cheney did not know the identity of the donor.
The aide said Cheney had been waiting for a transplant for more than 20 months, adding that the he does not know the identity of the donor.
In 2010, Cheney suffered his fifth heart attack since the age of 37. He had bypass surgery in 1988 and had a pacemaker implanted in his chest in 2001.