Female members of the Royal Family are to be given equality with men in the rules of succession, under constitutional changes agreed yesterday by the 16 Commonwealth nations where the Queen is head of state.
As a result, if the first child of the Duke and Duchess of Cambridge is a girl, she will take precedence over any younger brothers in the order of succession.
Laws banning royals from acceding to the throne if they are married to a Roman Catholic will also be abolished, though the monarch will still have to be a member of the Church of England.
Announcing the changes at the Commonwealth Heads of Government Meeting in Australia, David Cameron said the historic rules were "at odds with the modern countries that we have become".
He added: "Put simply, if the Duke and Duchess of Cambridge were to have a little girl, that girl would one day be our queen."
Reform of the succession rules, which date to the 17th century, has long been seen as overdue in an age of greater equality between genders and faiths.
But putting future princesses on an equal footing with their brothers will require amendments to much historic legislation, including the 1701 Act of Settlement and 1689 Bill of Rights, as well as laws in Commonwealth states including Canada, Jamaica, and Belize.
Any legislative changes will apply to the heirs of the Prince of Wales, so the children of William and Catherine will be affected whether or not they are born before the process of amending laws is completed.
The Most Reverend Vincent Nichols, Archbishop of Westminster and president of the Catholic Bishops' Conference of England and Wales, said he welcomed the change.
"This will eliminate a point of unjust discrimination against Catholics and will be welcomed not only by Catholics but far more widely," he said.
The pressure group Republic, which is campaigning for an elected head of state, dismissed plans to reform the rules of succession as "absurd".
Its campaign manager, Graham Smith, said: "The monarchy discriminates against every man, woman and child who isn't born into the Windsor family. To suggest this has anything to do with equality is utterly absurd."
A Buckingham Palace spokeswoman would not comment on the development, saying only that "it was entirely a matter for the 16 realms".
Mr Cameron also announced the creation of a Diamond Jubilee Trust, chaired by the former Prime Minister Sir John Major, to help those in need across the Commonwealth.
Sir John said the Trust would "create an enduring tribute to one of our longest-serving monarchs, who is held in enormous affection by many millions of people around the Commonwealth and the wider world".
Mr Cameron praised the Queen's "60 years of extraordinary public service" and said Britain would make a multimillion-pound donation to the Trust.