The royal baby is a boy.
Meghan finally gave birth around a week after her due date.
Her husband The Duke of Sussex was present for the birth, which happened at 5.26am.
Speaking from Windsor, a beaming Prince Harry told delighted reporters: ‘I’m very excited that Meghan and myself had a baby boy early this morning, a very healthy boy.
‘Mother and baby are doing incredibly well. It’s been the most amazing experience I could ever possibly imagine.
‘I can’t possibly imagine how any woman does what they do, what they do is beyond comprehension, but we are both absolutely thrilled and so grateful for all the love and support from everybody out there.’
He added: ‘It’s been amazing, we just wanted to share this with everybody.
‘Still thinking about names. The baby is a little bit over due so we’ve had a little time to think about it.
‘That’s the next bit, but for us, we will seeing you guys in two days time as planned as a family to be able to share with it you guys, so everybody can see the baby.
‘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.’
Buckingham Palace confirmed the happy news on social media.
In a statement, it said: ‘We are pleased to announce that Their Royal Highnesses The Duke and Duchess of Sussex welcomed their firstborn child in the early morning on May 6th, 2019.
‘Their Royal Highnesses’ son weighs 7lbs. 3oz.
‘The Duchess and baby are both healthy and well, and the couple thank members of the public for their shared excitement and support during this very special time in their lives.’
Meghan went into labour at around 5am on Monday.
The baby’s sex was a surprise for the Duke and Duchess, who had chosen not to find out what they are having until after the birth.
The baby is the Queen’s eighth grandchild.
The baby prince or princess is also be seventh in line to the throne, after Prince Charles, Prince William, Prince George, Princess Charlotte, Prince Louis and Prince Harry.
Meghan’s doting mother Doria was at her daughter’s side for the birth at Frogmore House in Windsor.
Both Harry and Meghan have close family ties to Malta, as 89.7 Bay revealed last year.