"I'm delighted to hear that mother and child are doing well," Thomas Markle said in a statement to The Sun. "I am proud that my new grandson is born into the British royal family and I am sure that he will grow up to serve the crown and the people of Britain with grace, dignity, and honor."
Baby Sussex, whose name is yet to be revealed, is Thomas' sixth grandchild.
His daughter, Samantha, and son, Thomas Jr., from whom Duchess Meghan is also estranged, have five children between them.
Duchess Meghan and Prince Harry have been estranged from Thomas, 74, since he missed their royal wedding last May and repeatedly spoke about the couple to the press.
Last month, sources close to the former Hollywood lighting director told reporters that Thomas had no plans to travel overseas to visit his grandchild.
Thomas is reportedly persona non grata at the palace and claims he has not been able to reach Duchess Meghan, alleging that she is in a "cone of silence."
A royal expert previously speculated that Thomas may never meet Prince Harry and Duchess Meghan's baby, claiming, “I can’t think for a moment that Thomas Markle will ever be able to meet his grandson or granddaughter.”
Another said that Duchess Meghan "moved on" from her family drama and is focusing solely on motherhood.
Duchess Meghan sent Thomas a handwritten letter begging him to stop speaking to tabloids — which he later released to a tabloid, allegedly to clear his name after he'd felt wronged by several of her friends who'd spoken about their difficult relationship in the media.
Thomas previously also confessed to hanging up on Prince Harry when the Duke of Sussex confronted him about staging paparazzi photos leading up to the royal wedding, a move that was orchestrated by Duchess Meghan's estranged sister Samantha.