David Bennett, 57, is doing well three days after the experimental seven-hour procedure in Baltimore, doctors say.
The transplant was considered the last hope of saving Mr Bennett's life, though it is not yet clear what his long-term chances of survival are.
"It was either die or do this transplant," Mr Bennett explained a day before the surgery.
"I know it's a shot in the dark, but it's my last choice," he said.
Doctors at the University of Maryland Medical Center were granted a special dispensation by the US medical regulator to carry out the procedure, on the basis that Mr Bennett - who has terminal heart disease - would otherwise have died.