The duchess is not yet 12 weeks pregnant, Clarence House told CNN, so the palace is not announcing a due date for the child.
William and Catherine's child will be next in line to the British throne after William, regardless of whether it is a boy or a girl.
Planned changes to the law of succession that end the tradition of a boy jumping over an elder sister are already de facto in effect, the British Cabinet Office said.
Deputy Prime Minister Nick Clegg said Tuesday that all 16 countries that recognize the British monarch as their head of state have formally agreed to the change and British lawmakers will change the rules as soon as possible.
Clegg also said that the change in succession will allow someone in line to the throne to marry a Catholic -- but not to be a Catholic. The Church of England is the nation's official church. It split from the Roman Catholic Church in the 16th century.