Meghan, the Duchess of Sussex and wife of Britain's Prince Harry, has gone into labour, Sky News has reported.
Sky News reporter Rhiannon Mills said Meghan had gone into labour early on Monday and that Harry was with her.
Buckingham Palace has since confirmed the news.
The child, the couple's first, will be seventh-in-line to the British throne.
Queen Elizabeth's grandson Harry, 34, and Meghan, 37, a US-born former actress, married in a lavish ceremony at the monarch's Windsor Castle home in May last year.
The baby will be the eighth great grandchild of the 93-year-old queen, the world's longest-reigning monarch, and could be entitled to hold joint British and American citizenship according to nationality rules.
However, the child will not automatically be a prince or a princess as any such title will have to be bestowed by the queen by issuing what is known as a letter patent.