Kensington Palace said Catherine was admitted to the Lindo Wing at St Mary's Hospital, Paddington, in central London.
Catherine has been on maternity leave since making a last royal visit to a charity lunch in London on 22 March.
The duchess travelled by car from Kensington Palace to St Mary's with The Duke of Cambridge.
The baby will be fifth in line to the throne - behind Prince Charles, Prince William and her siblings Prince George, four, and Princess Charlotte, aged two.
The duchess's pregnancy was announced in October, with the baby due in April.
As with her previous two pregnancies, Catherine, 35, has suffered from hyperemesis gravidarum, or severe morning sickness.
The child will be the Queen's sixth great-grandchild.