The first born of the Duke and Duchess of Cambridge will succeed the throne after Prince William, whether they are male or female
All Commonwealth countries have agreed to press ahead with a bill ending discrimination against women in the succession to the British throne.
Deputy Prime Minister Nick Clegg said the government would now introduce the Succession to the Crown Bill in the House of Commons as soon as possible.
It means the first child of the Duke and Duchess of Cambridge will become monarch whether it is a boy or girl.
The duchess, whose pregnancy was announced on Monday, is in hospital.
She is spending her second day in the private King Edward VII Hospital in central London with acute morning sickness.
The new legislation will end the principle of male primogeniture, meaning male heirs will no longer take precedence over women in line to the throne.
It will also end the ban on anyone in the line of succession marrying a Roman Catholic.