Simon Bramhall pleaded guilty last month to two counts of assault in a case a prosecutor called "without legal precedent in criminal law."
Bramhall used an argon beam coagulator, which seals bleeding blood vessels with an electric beam, to mark his initials on the organs.
The 53-year-old surgeon resigned from Queen Elizabeth Hospital in Birmingham in 2014 after another doctor discovered what he'd done.
The hospital said there had been "no impact whatsoever" on the success of the operations.
The judge accepted that the patients were not physically harmed but said one had suffered "extreme and enduring" psychological stress after learning what had happened.
"What you did was an abuse of power and a betrayal of trust that these patients had invested in you," the judge said.