An aide to Cheney said he had been waiting for a transplant for more than 20 months and does not know the identity of the heart donor.
"Although the former vice president and his family do not know the identity of the donor, they will be forever grateful for this lifesaving gift," aide Kara Ahern said in a written statement that was authenticated by several close associates of the former vice president.
Cheney was recovering Saturday night at the Intensive Care Unit of Inova Fairfax Hospital in Falls Church, Va., after surgery earlier in the day.
Cheney suffered a heart attack in 2010, his fifth since the age of 37. He had bypass surgery in 1988, as well as two subsequent angioplasties to clear narrowed coronary arteries.
In 2001, he had a special pacemaker implanted in his chest.