The 37-year-old royal - who was known as Meghan Markle before her marriage to 34-year-old Harry - and her husband welcomed a 7lb 6oz son into the world on Monday morning and now her dad has sent the couple his best wishes and is certain that the royal baby boy will serve the people of Britain with "grace, dignity and honour".
In a statement, Thomas, 74, told The Sun newspaper: "I'm delighted to hear that mother and child are doing well. 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 the 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."
The 74-year-old retired Hollywood lighting director - who lives in Rosarito, Mexico - has six grandchildren in total. His other two children, Samantha, from Virginia, and Thomas Jr., who resides in Oregon, have five kids between them, all of whom live the US.
Thomas has not spoken to his daughter Meghan since she got married to Harry last May, although there has been correspondence by letter. He was unable to attend the ceremony at St George's Chapel at Windsor Castle after suffering a heart attack in the lead up to the big day.
Harry - who is the son of heir to the British throne Prince Charles and younger brother of Prince William - confirmed the happy news to assembled media and praised his wife for how she coped during the labour.
Harry - whose mother is the late Princess Diana - said: "I'm very excited to announce that Meghan and myself had a baby boy earlier this morning, a very healthy boy. Mother and baby are doing incredibly well. It's been the most amazing experience I could ever have possibly imagined.
"How any woman does what they do is beyond comprehension, but we're both absolutely thrilled and so grateful for all the love and support from everybody out there. It's been amazing, so I just wanted to share this with everybody ... I haven't been at many births, this is definitely my first birth but it was amazing, absolutely incredible.
"I'm so incredibly proud of my wife and as every father and parent would ever say, your baby is absolutely amazing, but this little thing is absolutely to die for so I'm just over the moon."
The couple are yet to choose a name for their son.