* Duchess of Sussex gives birth to baby boy at 4.26pm Monday NZT
* Prince Harry by his wife's side for birth and says baby is "to die for"
* Child weighs 7lbs 3oz (3.26kg) - the couple are yet to decide on name
* Little boy seventh in line for throne - why he's not automatically a prince
* What's in a name? Arthur a favourite bet
Meghan Markle has given birth to a baby boy with her husband Prince Harry by her side after going into labour on Monday afternoon (NZT).
Speaking from Windsor, the Duke of Sussex said the child was "absolutely to die for" and he is "so proud" of his wife.
Buckingham Palace said the baby was delivered at 5.26am local time (4.26pm, Monday NZT) and weighs 7lbs 3oz (3.26kg). The couple have not yet chosen a name for their son.
The beaming Prince said: "I'm very excited to announce that Meghan and myself had a baby boy earlier this morning, a very healthy boy. Mother and baby are doing incredibly well. It's been the most amazing experience I could ever have possibly imagined.
"How any woman does what they do is beyond comprehension, but we're both absolutely thrilled and so grateful to all the love and support from everybody out there. It's been amazing, so we just wanted to share this with everybody."
Asked if they had any names yet, Harry said: "Still thinking about names. The baby is a little bit overdue, so we've had a little bit of time to think about it.
"That's the next bit, but for us I think we will be seeing you guys in probably two days' time as planned as a family to be able to share it with you guys and so everyone can see the baby."
Asked what it was like to be present for the birth, he laughed and said: "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 incredibly proud of my wife.
"As every father and parent will 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."
A traditional easel bearing the royal birth notice was placed outside the palace.
The "overjoyed" couple also confirmed the arrival of the new seventh in line to the throne in a statement posted on Instagram, thanking the public for sharing in an "exceptionally joyful" time in their lives.
Bookies are currently taking bets on the name of the baby, which will be announced at a later date.
Arthur is the 5-1 favourite with leading bookmaker Coral. Philip is next best at 6-1, Albert and James are 8-1, while Alexander and Alfred are 10-1.
Buckingham Palace said in a statement: "Her Royal Highness The Duchess of Sussex was safely delivered of a son at 0526hrs (4.26pm Monday NZT).
"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' mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with their Royal Highnesses at Frogmore Cottage."
On Instagram, the couple wrote: "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.
"More details will be shared in the forthcoming days."
The couple had announced earlier a low key photo-call would be held "around two days afterwards".
Meanwhile, well-wishers are cracking open champagne and waving Union Jacks outside Windsor Castle to celebrate the birth of Baby Sussex.
The couple had maintained an element of secrecy around the arrangements for the birth and said they would share news of their baby's arrival "once they have had an opportunity to celebrate privately as a new family".
Members of the international press have been assembled in Windsor for several weeks awaiting news that the baby is on its way, with American television networks updating their viewers daily.
The baby is understood to be around a week overdue, and the Duchess, who is 37, was said to be "comfortable and content" as she waited in her new home at Frogmore Cottage with her husband and mother by her side.
The Duchess reportedly chose a female-led team to support her during the birth, with the royal household doctors on hand to help if necessary.
A previous statement, released by Buckingham Palace said: "The Duke and Duchess of Sussex are very grateful for the goodwill they have received from people throughout the United Kingdom and around the world as they prepare to welcome their baby.
"Their Royal Highnesses have taken a personal decision to keep the plans around the arrival of their baby private. The Duke and Duchess look forward to sharing the exciting news with everyone once they have had an opportunity to celebrate privately as a new family."
A royal correspondent revealed on Friday, April 26 that Meghan's due date was the day before.
On Good Morning Britain ITV's royal editor Chris Ship said the baby arrival was "imminent".
In the UK, bookies were claiming Meghan would give birth in May, after Prince Harry was seen stepping out with Kate Middleton at Anzac Day commemorations at Westminster Abbey.
"We were as surprised as everyone else that Harry decided to attend a public event as we assumed the baby was imminent," Rupert Adams, a William Hill spokesman, told the Mirror in the UK.
"We are now odds-on that the baby will not arrive until May."
The odds were also on her having a girl.
British betting company Ladbrokes also had the shortest odds on the littlest Windsor being named Albert.
But it had also been suggested she might decide to follow in the footsteps of Canadian Autumn Phillips, wife of Harry's cousin (and Princess Anne's son) Peter Phillips, and choose something a little more contemporary. These days, Savannah and Isla Phillips are regularly spotted getting up to all sorts of naughty japes with their third cousin Prince George, often at the polo.
Matilda, Winston and Spencer were all rumoured to be on the table.
The baby, who will be seventh-in-line to the throne, has already made its presence felt on social media after the Sussexes' official Instagram account thanked fans for their charity donations in his or her name.
A post read: "On behalf of The Duke and Duchess (and Baby Sussex), we thank you so much."