LONDON (CNN) — The hospital, next to Paddington Station in London, is where William and his brother Prince Harry were born.
The duchess' mother, Carole Middleton, was expected to be on hand at the hospital.
The baby's name may be announced when the family leaves the hospital, CNN royal correspondent Max Foster reported. Prince William's name was announced a few days after birth, his brother Harry's on departure from hospital.
Some British parents have delayed naming their newborns in recent days in hopes of either copying or avoiding the royal name, he said.
British bookmakers favor the names Alexandra, Charlotte, Elizabeth, Victoria, Grace, James and George. The field is open for both boys' and girls' names because royal sources said the parents did not want to know their child's sex in advance.
The child's title will be His or Her Royal Highness Prince or Princess (the baby's name) of Cambridge, St. James's Palace said this month.
-- Journalist David Simpson contributed to this report.