Harry said he was ecstatic about the birth of their first child and promised that more details — such as the baby's name — will be shared in the coming days.
"This little baby is absolutely to die for," he said. "I'm just over the moon."
Ryan Seacrest was among the first celebrities to share his thoughts on the birth of the royal baby saying: "It's a boy! Congrats to Meghan Markle and Prince Harry. The royal baby is 7th in line to the British throne...and the latest entry in the race for the iron throne," he wrote referencing the successful TV series "Game of Thrones".
"Congratulations to the Duke and Duchess of Sussex on the birth of their baby boy. May God bless the new family with love, health and happiness. #RoyalBaby," the Archbishop of Canterbury tweeted.
Soon after, the royal family, including Prince William and Kate Middleton, released a statement congratulating the couple on the birth.
"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, The Duke and Duchess of Cambridge, Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer have been informed and are delighted with the news," it read.
"The Duchess' mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with Their Royal Highnesses at Frogmore Cottage."
Princess Eugenie's father, Prince Andrew, the Duke of York, also shared Meghan and Harry's birth announcement, along with the caption, "Congratulations to The Duke and Duchess of Sussex on the safe delivery of your baby boy!"
Meghan's estranged family members including her half-sister Samantha Markle, and her father Thomas Markle, have yet to comment publicly on the birth.
Michelle Obama said she and Barack can't wait to meet the baby boy.
Some of Meghan's former Suits co-stars, including Sarah Rafferty and Patrick Adams, also took to social media to welcome the arrival of royal baby Sussex.
Ellen DeGeneres sent her well wishes with a joke about being in line at a grocery store.
While the royal family cannot accept material gifts, Prime Minister Jacinda Ardern said New Zealand instead sent various donations to charity and took part in environmental restoration work.
"I can tell you that on behalf of New Zealanders, we'll be making a donation to Little Sprouts, which is an organisation that prepares baby boxes for families in need," she said on the AM show.
"We'll also be purchasing 10 native trees that will be planted as part of trees that count specially for newborn babies and I think they're planted around the time of Matariki.
"I hope New Zealanders think those are suitable gifts on their behalf in recognition of the new baby."