Prime Minister David Cameron said "the great strength of our constitutional approach is its ability to evolve".
In future, female members of the Royal Family will have the same rights of succession to the throne as men. This means that if the Duke and Duchess of Cambridge’s first child is a girl, she will succeed to the throne ahead of any younger brothers she may have.
The current rule which says that anyone who marries a Roman Catholic can’t become monarch will also be abolished.
Mr Cameron announced the changes in his press conference with Prime Minister Gillard at the Commonwealth Heads of Government Meeting (CHOGM), currently taking place in Perth, Western Australia.
It followed a meeting of all 16 Realms (nations of which Queen Elizabeth II is monarch), jointly hosted by Mr Cameron and Prime Minister Gillard.
The Prime Minister said:
“The great strength of our constitutional approach is its ability to evolve.
“Attitudes have changed fundamentally over the centuries and some of the out-dated rules - like some of the rules of succession - just don’t make sense to us any more.
“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.”
Mr Cameron also said:
“People have been talking about changing the rules for some time, but when there are 16 countries sharing the same head of state and each have their own constitutional, legal and political concerns, it is absolutely right that we should all discuss this together.
“That is why I asked Prime Minister Gillard for the opportunity to chair this meeting today with the heads of government of all 16 nations. “I am very pleased to say that we have reached a unanimous agreement on two changes to the rules of succession.
“Firstly, we will end the male primogeniture rule, so that in future the order of succession should be determined simply by order of birth, and we have agreed to introduce this for all descendants of the Prince of Wales.
“Put simply, if the Duke and Duchess of Cambridge have a little girl, that girl will one day be our queen. “Second, we have agreed to scrap the rule which says that no-one who marries a Roman Catholic can become monarch. “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. After all, they are already quite free to marry someone of any other faith.
“We agreed today that this has to change.”
New Zealand will now chair a working group, which will discuss the best way of accomplishing this reform in all the countries concerned.
In the United Kingdom, legislation will need to be passed in order to change the rules on succession. The Government is still looking into exactly what legislation needs to be amended, but the list includes the Bill of Rights, the Coronation Oath Act, the Act of Settlement, the Act of Union with Scotland, the Accession Declaration Act, Princess Sophia’s Precedence Act, Royal Marriages Act, the Union with Ireland Act and the Regency Act.
The Commonwealth Heads of Government Meeting (CHOGM) is taking place in Perth, Western Australia. The meeting is held every two years and is attended by heads of government from Commonwealth nations.