Doctors said the Da Vinci robot is remotely controlled by surgeons who are given a high definition view of the heart through a sophisticated camera.
Twenty-two-year old Natalie Jones from Stourbridge was the first patient to have the procedure, involving a hole in her heart repaired, at the New Cross Hospital in Wolverhampton.
A team of doctors including Moninder Bhabra claim the operation is safer for patients than conventional surgery, the 'BBC News' reported.
Normal heart surgery involves cutting open the breast plate, but the robotic arms are inserted by making incision between the patient's ribs.
A surgeon is given a 3-D, high-definition view of the heart and can move the arms using a control panel. Each time they move their hand 3mm, the robot arm moves just 1mm.
"There is less pain and patients are able to return home to their normal activities far sooner," heart surgeon Stephen Billing said.
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Jones had a 3.5cm (1.3inch) hole in her heart repaired during surgery which lasted nine hours.
"I was scared, but I chose the robot surgery because I didn't want to have a large scar and I liked the idea of being the first," she said.
A more complex procedure - a mitral valve repair - was carried out on 43-year-old Paul Whitehouse from Halesowen.
Surgeons said that Whitehouse might be able to go back to work as a self-employed builder after two months instead of the normal six months recovery time.
The hospital hopes to carry out 30 mitral valve repairs a year using the robot that is already employed in other operations at the hospital.
UK is the third country in Europe after Sweden and Finland to perform open-heart surgery using robots, the report said.
A team of surgeons including Bhabra and Billing underwent extensive training in Finland before the first procedure.
"I accept money is tight within the NHS, but we can't be left behind by the rest of the world in developing what we are doing in surgery and other aspects of health care," said Bhabra.