The 37-year-old safely delivered her first child, just minutes before sun rise at London time today.
Here's the Buckingham Palace statement in full: "Her Royal Highness, the Duchess of Sussex was safely delivered of a son at 0526hrs.
"The baby weighs 7lbs 3oz."
The Duke of Sussex was present for 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.
"The Duchess's mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with their Royal Highnesses at Frogmore Cottage.
"Her Royal Highness and her child are both doing well."
Speaking from Windsor, the Duke of Sussex said: "I'm very excited to announce that Meghan and myself had a baby boy this morning, a very healthy baby boy."
A smiling Harry added: "Mother and baby are doing incredibly well. It’s been the most amazing experience I can ever have possibly imagined."
How any woman does that, what they do is beyond comprehension.
"We’re both absolutely thrilled and so grateful to all the love and support of everybody out there, it's been amazing, so I just wanted to share this with everybody."
‘’Still thinking about names but, yeah, the baby is a little overdue so we’ve had a little bit of time to think about it, but that’s the next bit’’.
"We’ll be able to see you in two days' time as planned and be able to share it with you as a family and share it with you guys and so everyone can see the baby.
“I haven’t been at many births, this is definitely my first birth, it was amazing, absolutely incredible and as I said, I’m so incredible proud of my wife and as every father and parent would ever say, your baby is absolutely amazing, so this little thing is absolutely to die for, so I’m over the moon’’.
He said they had not yet decided on a name for the child and would make their first appearance as a family in a couple of days' time.
The Duke and Duchess's Instagram account @SussexRoyal also announced the birth saying: "It's a boy! Their Royal Highnesses the Duke and Duchess of Sussex are overjoyed to announce the birth of their child."Prime Minister Theresa May said: "Congratulations to the Duke and Duchess of Sussex on the arrival of their baby boy. Wishing you all the best at this happy time."
Meghan is now expected to take maternity leave for several months, and Harry will also have some time off as paternity leave.
The new baby will grow up at the couple's new Windsor home, Frogmore Cottage , which has just undergone a huge renovation.
Meghan and Harry moved in last month, later than planned due to delays in the building work.
During her pregnancy she told a well-wisher she was due in April, but as it traditional with royal babies the couple decided to keep the exact due date a secret.
The new mum was last seen at an official engagement last month when the couple went to sign the book of condolence to the 50 people killed in the horrific New Zealand mosque shootings.Prince Harry has attended a number of official engagements this week, including an Anzac service with Kate and the London Marathon , which was kept secret in case the baby arrived.
Meghan and Harry's tied the knot at St George's Chapel in Windsor in May last year. In their engagement interview they said they were keen to start a family.
Prince Harry said: "Of course, one step at a time and hopefully we will start a family in the near future."
During her pregnancy Meghan kept well-wishers up-to-date with how she was feeling and the couple regularly told people they were very excited to become parents.
During a chat with people at Sydney's Bondi Beach she compared pregnancy to being jetlagged and said she was doing yoga every morning to help with the symptoms.
She said: "It's like having jet lag without actually travelling".