Former vice president Richard B. Cheney was released from Inova Fairfax Hospital on Tuesday, 10 days after receiving a new heart from an undisclosed donor and making a “remarkable” recovery that his doctor said was much faster “than anyone could have hoped for.”

Cheney, 71, had a transplant operation March 24 after a 20-month waiting period during which he was kept alive with an implanted pump that helped his weakened heart keep beating.

“His recovery was remarkable and completely uneventful,” said Jonathan Reiner, Cheney’s longtime cardiologist at George Washington University Hospital.

“He has been walking, he has climbed stairs, and he feels terrific,” he said. “I think his recovery after the surgery far exceeded the most optimistic projections. . . . It is far better than anyone could have hoped for.”

Cheney and his family thanked his doctors at Inova and GWU hospitals, the nursing staff at the Inova heart center’s intensive-care unit, and the donor and donor’s family “for this remarkable gift,” aide Kara Ahern said in a statement announcing Cheney’s departure from the hospital.

Reiner gave special acknowledgment to “world-class” care from Cheney’s surgeons, Alan Speir and Anthony Rongione, and Shashank Desai, medical director of Inova’s heart-transplant program.

Cheney’s odds of survival are good. About 70 percent of people who have the kind of mechanical device Cheney did — a continuous-flow “left-ventricular assist device” (LVAD) — survive at least six years after they get a new heart, according to data compiled by the Texas-based International Society for Heart & Lung Transplantation.

Even 10 years with a good quality of life “would not be an unreasonable expectation,” Reiner said.

Cheney will be monitored for infection and bleeding. He will also be assessed regularly, through heart-muscle biopsies, to make sure his body is not rejecting the donor heart, Reiner said. He will undergo a gradual progression in physical activity, similar to patients recovering from other kinds of heart surgery.

Cheney waited nearly two years for the transplant. His lifelong history of heart disease includes five heart attacks, with the first one in 1978, when he was 37, and the most recent one in 2010. After that attack, surgeons at Inova’s heart institute implanted the pump, a rapidly growing strategy for patients with advanced heart disease.

About 3,000 VADs are put into Americans each year. About 2,500 heart transplants are performed annually in North America, about the same as in 1994.

More than 3,100 people are on a national waiting list to receive a new heart, according to the United Network for Organ Sharing. Who gets a donor heart depends on many variables. The most important one is a person’s clinical condition and immediate availability for surgery.

According to UNOS, 332 people older than 65 received a new heart last year. The majority of transplants occur in 50-to-64-year-olds.

Reiner said Cheney did not receive special treatment. “It didn’t happen. It couldn’t happen. And there is no way to make it happen,” he said. “These lists are managed by autonomous committees and regional transplant organizations.”

Cheney was on one waiting list, he said, at Inova Fairfax. The median waiting time for a heart transplant there is nine months, according to the Scientific Registry of Transplant Recipients, a national database of transplantation statistics.

Reiner declined to provide specifics about Cheney’s insurance, saying only, “The care he received is available to most Americans over the age of 65.”

Staff writer David Brown contributed to this report.