The 31-year-old Duchess of Cambridge travelled by car from the palace to St Mary's in Paddington, west London, with her husband.
"The notification has gone out that she is in the early stages of labour after being admitted to the Lindo wing this morning," the Kensington Palace official said.
The couple does not know the gender of their first child, who will be third in line to the throne.
BBC reported that there was likely to be no more news until the official announcement of the birth.
The world's press have been camped outside St Mary's for days in anticipation of the birth.
The due date had never been officially announced but had widely been expected to be mid-July.
Photograph: Reuters