The child, who was born in the Lindo Wing of St Mary's Hospital, central London, is fifth in line to the throne and the Queen's sixth great-grandchild.
The new arrival, who is the third child of Catherine and the Duke of Cambridge, was born at 11:01 BST weighing 8lbs 7oz.
A Kensington Palace statement said Catherine and her new son are "both doing well".
William was present for the birth, the palace added.

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The Canadian prime minister is in London for the Commonwealth Heads of Government Meeting (CHOGM).

An EU-Canada trade deal, known as CETA, came into force last year.

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“He has a habit of... telling lies, sometimes big, sometimes casual and insisting that the people around him repeat them and believe them and that stains any human," he said.

In a wide-ranging interview Mr Comey told Newsnight's Emily Maitlis that he doesn't believe the president has anyone around him to stop his impulsive behaviour.

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The BBC's Steve Rosenberg speaks to retired Russian scientist Vladimir Uglev who says he manufactured a Novichok nerve agent.

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A "good relationship" was formed at the meeting last week, Mr Trump tweeted on Wednesday.
News of the visit first emerged on Tuesday. US officials were quoted as saying the aim was to prepare a summit between Mr Trump and Mr Kim.
Mr Trump had earlier alluded to high-level direct talks with Pyongyang.
But the unexpected and clandestine meeting marks the highest level US contact with North Korea since 2000.

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Southwest Airlines Flight 1380 made an emergency landing in Philadelphia after a window, wings and fuselage were damaged in the incident, officials say.
One woman was killed and seven others needed medical treatment.

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Amelia was left traumatised after witnessing the deadly bomb blast at an Ariana Grande concert in Manchester in May 2017.

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