The newborn weighed 7 pounds and 3 ounces. The baby was born at 5:26 a.m. local time, according to Buckingham Palace.
Both mom and baby are "doing incredibly well," Prince Harry said in brief remarks outside Frogmore Cottage, the Windsor home where he and Meghan will raise their son.
"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," Buckingham Palace said in a statement.
Meghan's mother, Doria Ragland, is with her and Prince Harry at Frogmore Cottage, according to Buckingham Palace. The Los Angeles-based Ragland is "overjoyed by the arrival of her first grandchild," the palace said.
Meghan went into labor in her 41st week of pregnancy, one week past her due date. Harry, 34, and Meghan, 37, will share more details about the baby's name "in due course," according to Buckingham Palace.
"I’m so incredibly proud of my wife," Harry said Monday. "And as every father and parent would ever say, you know, your baby is absolutely amazing, but this little thing is absolutely to die for. So I’m just over the moon."
He is also the fourth grandchild for Prince Charles and the eighth great-grandchild for Queen Elizabeth. Meghan and Harry's son will share a close birthday to his cousin, Princess Charlotte, who turned 4 on May 2.
Baby Sussex appears to be the first mixed race child born into the royal family, although historians are divided. Meghan was born to a white father and a black mother and grew up as a biracial child in Los Angeles.
Some royal historians have pointed out that when Queen Charlotte married King George III in the 1700s, he was believed to have descended from the black branch of the Portuguese royal family. The couple had 15 children, according to the British royal family's website.
The son of the Duke and Duchess of Sussex, could hold dual American and British nationality, a first for a royal baby.
Meghan, a California native, is reportedly still waiting for her British citizenship application to be approved.
"From what I understand, Harry and Meghan will have to acquire documentation for their child to prove U.S. citizenship and it’s not clear if they will do that but of course the option is there," said ABC News royal contributor Victoria Murphy.
Harry and Meghan as parents
Prince Harry married Meghan last May. Five months later, they announced the pregnancy as they embarked on their 16-day tour of Australia, New Zealand Fiji and Tonga.
"I've got a kid inside of me, I want to keep that, I adore kids," he added. "I enjoy everything that they bring to the party, and they just say what they think."
Meghan's friends have also described her as someone with a maternal instinct who is genuine in her interactions, particularly with kids.
“When you see her at walkabouts, when she crouches down to talk to the kids and genuinely has real conversations with people, that’s Meg,” a former costar of Meghan's told People magazine in February. “That’s how she crouches down with our kids at home. That’s how she plays with them. That’s how she engages with people and how she always has.”