In this photo provided by the University of Maryland School of Medicine, members of the surgical team show the pig heart for transplant into patient David Bennett in Baltimore. Photo / AP
David Bennett, 57, from Maryland, underwent the groundbreaking surgery at the University of Maryland Medical Center in Baltimore last week.
According to the Washington Post, Bennett was convicted in 1988 of stabbing Edward Shumaker in a bar.
Shumaker spent the next two decades in a wheelchair, before having a stroke and dying aged 40.
His sister, Leslie Shumaker Downey, told the Washington Post: "Ed suffered. The devastation and the trauma, for years and years, that my family had to deal with.
A jury acquitted him of intent to murder but found him guilty of battery and carrying a concealed weapon.
The judge reportedly called it an act of "extreme violence" and sentenced him to 10 years in jail.
The victim's family also sued him and he was ordered to pay $3.4 million in damages, but they said it was never paid.
In a statement, the hospital said it provided "lifesaving care to every patient who comes through the doors based on their medical needs, not their background or life circumstances".
A spokesman said: "This patient came to us in dire need and a decision was made about his transplant eligibility based solely on his medical records."
Over 100,000 Americans are currently waiting for organ transplants. Around 6000 patients die each year before getting one.
Scott Halpern, a professor of medical ethics at the University of Pennsylvania, told the Washington Post: "We have a legal system designed to determine just redress for crimes.
"And we have a healthcare system that aims to provide care without regard to people's personal character or history."
After his release from prison, Bennett worked as a handyman for the Pittsburgh Steelers American football team.
Dr Bartley Griffith, who led the transplant team, said on Wednesday: "The new heart is still a rock star. It seems to be reasonably happy in its new host. It has more than exceeded our expectations."