A statement from the former vice president's office said the 71 year old is now recovering in the intensive care unit of Inova Fairfax Hospital in Falls Church, Va., outside Washington.
The statement said Cheney had been on the transplant list for 20 months and did not know the identity of the donor.
The former Vice President has had a long history of heart problems. He had a unique kind of artificial heart put in in 2010 after having had multiple heart attacks over his lifetime.
Our thoughts and prayers are with the former Vice President and his family and we hope for a speedy recovery.