A statement from the palace has been issued, confirming the arrival this morning.
It says: ‘Her Royal Highness The Duchess of Sussex was safely delivered of a son at 5.26am.
'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.’
The name of the baby, which is seventh in line to the throne, will be announced at a later date.
Harry and Meghan's baby is seventh in line to the throne and the Queen and the Duke of Edinburgh's eighth great-grandchild, and a fourth grandchild for the Prince of Wales.
The baby's sex was a surprise for the couple, who chose not to find out what they were having.
Ahead of the birth, the duke and duchess made a decision to keep the arrangements private, amid speculation they had opted for a home birth at their new home Frogmore Cottage, close to the Queen's Windsor Castle home.
Meghan was last seen on an official engagement on March 19 when she signed a book of condolences in London with Harry for the victims of the Christchurch terror attack.
The American former actress and the duke moved into their renovated home Frogmore Cottage on the Windsor Estate at the beginning of April, as they prepared for their baby's arrival.
Meghan is believed to have been overdue, and there had been speculation the duchess was looking likely to be induced.
Harry's trip to Amsterdam and overnight stay away on Wednesday was cancelled on Friday, with Buckingham Palace saying it was due to logistical concerns surrounding press coverage of royal events, rather than the baby.
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.’
The couple married at a ceremony in Windsor in May last year.