Meghan Markle's Dad Thomas Markle is Alert and Out of Surgery

3:05 PM PT -- Thomas says, "I'm ok. It will take a long time to heal. Staying in the hospital a few more days. Not allowed to get excited."

Meghan Markle's dad, Thomas, appears to have successfully undergone heart surgery ... TMZ has learned.

We spoke with Thomas a few minutes ago and he seemed alert and coherent, telling us doctors implanted stents in his blood vessels ... he said he believes surgeons implanted 3 stents, but he wasn't sure.

He was scheduled to go into the OR at 7:30 AM.

As we reported, the surgery was necessary after Thomas experienced significant damage to his heart ... the result of a heart attack 8 days ago. Thomas told us Tuesday, "They [doctors] will go in and clear blockage, repair damage and put a stent where it is needed."

Thomas told TMZ Tuesday ... he had a change of heart and wanted to walk Meghan down the aisle, but realized it was not going to happen because of the surgery.