London (CNN) -- Sons and daughters of British monarchs will have an equal right to the throne under changes to the United Kingdom's succession laws agreed to Friday, British Prime Minister David Cameron said.
The leaders of the 16 Commonwealth countries that have the queen as head of state approved the changes unanimously at a Commonwealth of Nations summit in Australia, he said. The individual governments of those 16 countries still must agree to the changes for them to take effect.
The constitutional changes would mean a first-born girl has precedence over a younger brother. They also mean that a future British monarch would be allowed to marry a Catholic.
The laws would apply to any future children of Prince William and Catherine, the Duchess of Cambridge, who married this year.
Speaking alongside his Australian counterpart Julia Gillard in Perth, Cameron described Friday's agreement by the heads of government of the 16 nations as "something of a historic moment."
Attitudes have changed fundamentally over the centuries, he said in a televised address, and outdated rules should evolve with them.
"The idea that a younger son should become monarch instead of an elder daughter simply because he is a man, or that a future monarch can marry someone of any faith except a Catholic -- this way of thinking is at odds with the modern countries that we have become," he said.
"Put simply, if the Duke and Duchess of Cambridge were to have a little girl, that girl would one day be our queen."
Cameron also referred to plans to scrap the Act of Settlement, a law passed in 1701 which bans the UK monarch from marrying a Catholic. It was intended to ensure that Protestants held the throne and remained head of the Church of England.
"Let me be clear: the monarch must be in communion with the Church of England, because he or she is the head of that church, but it is simply wrong that they should be denied the chance to marry a Catholic if they wish to do so," Cameron said. "After all, they're already quite free to marry someone of any other faith."
Cardinal Keith O'Brien, leader of the Catholic Church in Scotland, said he welcomed the planned reform.
"I am pleased to note that the process of change, which I hope will lead to repeal of the Act has started and I look forward to studying the detail of the proposed reforms and their implications in due course," he said in a statement.
Richard Fitzwilliams, royal commentator and a former editor of International Who's Who, told CNN that the changes were vital if the monarchy was to adapt with changing times.
He said that "for decades, since the 1950s, there's been talk of doing this and nothing's actually happened," he said -- probably in part because it did not affect Prince Charles, Prince William and Prince Harry.
"Now the Duke and Duchess of Cambridge have said they want to start a family, this makes it urgent," he said.
While the constitutional change has to be made by parliament in the United Kingdom and the other 15 countries that have the queen as head of state, it is supported by Buckingham Palace, he said.
The situation where a younger brother would take precedence over a first-born sister is discriminatory under European law, he points out.
The legal changes relating to the marriage of the monarch to a Catholic will have to be handled sensitively, he added, because of the monarch's role as head of the Church of England, and involve several acts of parliament going back to the 17th and 18th centuries.
Britain is not the first European nation with a hereditary monarchy to take steps towards gender equality in its laws of succession.
Denmark changed its rules to make them gender neutral in 1953, enabling the current monarch, Queen Margrethe, to succeed to the throne.
Sweden followed suit in 1980, three years after the birth of Crown Princess Victoria, the current successor to the throne. Norway also accords equal rights of succession to royals born after 1990.
The issue of ending male primogeniture, or male heirs taking precedence over female ones, in the Spanish royal family was raised a few years ago, but has not yet resulted in constitutional change.
Buckingham Palace said it had no comment on the change to the law announced Friday, as it was a matter for the U.K. and Commonwealth governments.
Queen Elizabeth is in Australia for the three-day Commonwealth Heads of Government Meeting.
The Commonwealth is an association of 54 nations with ties to the United Kingdom. Only 16 share the queen as head of state.
CNN's James Partington and Laura Perez Maestro contributed to this report.