"I'm delighted to hear that mother and child are doing well," he said.
"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 honour.
"God bless he child and I wish him health and happiness. And my congratulations to my lovely daughter Duchess Meghan and Prince Harry - and God save the Queen."
Thomas Markle is said to be "terribly upset and deflated" over his absence from Meghan's life, and regards the birth of his grandchild as "bittersweet".
He recently issued a public plea for the Duchess to contact him after months of silence.
Watch this clip to hear what he had to say:
Another family member to publicly congratulate the new parents was Harry's uncle Prince Andrew, Duke of York, who's own children Princesses Beatrice and Eugenie were born at The Portland Hospital where Meghan reportedly delivered Baby Sussex yesterday.
Notably, the official social media channels for Kensington Palace - the account of Prince William and the Duchess of Cambridge - have yet to acknowledge the latest royal birth, save for a single retweet of the news from the British Royal Family Twitter page.
Harry and Meghan marked the recent birthdays of William and Kate's children Prince Louis and Princess Charlotte with personal comments on Instagram, but 9Honey reports the Cambridges may not return the favour.
