Cheney, 71, had the operation Saturday in Fairfax, Va.
Dr. Jonathan Reiner, Cheney's longtime cardiologist at George Washington University Hospital, told The Washington Post he visited the former vice president Sunday morning. He said Cheney "was doing exceedingly well."
Cheney is recovering in the intensive care unit of Inova Fairfax Hospital, the same hospital where he had a Left Ventricular Assist Device implanted in 2010. Cheney spent 20 months on a heart-transplant list, the hospital said.
"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," a statement released Saturday by the hospital said.
The Post said Cheney had his first heart attack in 1978, when he was 37.
The International Society for Heart & Lung Transplantation said about 70 percent of people who use a continuous-flow LVAD survive at least six years after they get a new heart, the newspaper reported.
"He's not too old to benefit from it," Reiner said told the Post.
Swim Week Miami Beach 2014 [PHOTOS]