Commonwealth national leaders also agreed at a summit in the western Australian city of Perth to lift a ban on monarchs marrying Roman Catholics, British Prime Minister David Cameron said.
Any one of the former British colonies could have vetoed the changes to the centuries-old rules that ensure that a male heir takes the throne ahead of older sisters.
"Attitudes have changed fundamentally over the centuries and some of the outdated rules - like some of the rules of succession - just don't make sense to us any more," Cameron told reporters in Perth.
"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 added.
Cameron made the announcement on the first day of a biennial meeting of 53 Commonwealth leaders.
Prime Minister Julia Gillard, Australia's first female leader and chairwoman of the summit, welcomed the decision.
"These things seem straightforward, but just because they seem straightforward to our modern minds doesn't mean we should underestimate their historic significance," Gillard told reporters.
Elizabeth II is head of state of Britain, Australia, New Zealand, Canada, Jamaica, Antigua and Barbuda, the Bahamas, Barbados, Grenada, Belize, St. Christopher and Nevis, St. Lucia, the Solomon Islands, Tuvalu, St. Vincent and the Grenadines and Papua New Guinea.
She opened the meeting of leaders representing 30 percent of the world's population on Friday by vowing to bring needed relevancy to the Commonwealth in a time of global uncertainty and insecurity.
The queen cited financial concerns, food supply insecurity and climate change among key issues she expected the forum to tackle.
"This Commonwealth meeting is, for its part, the perfect opportunity to address these issues and find responses for today's crises and challenges," she said in her opening address.
The queen also said the meeting would bring "new vibrancy" to the Commonwealth forum, which will be forced to defend itself against accusations of irrelevancy. A scathing report questioning its effectiveness will be presented to Commonwealth leaders during the summit.
Britain's government began the process of reviewing the rules of royal succession so that if Prince William's first child is a girl, she would eventually become queen. The review started before William married commoner Kate Middleton in April. She is now formally known as Catherine, Duchess of Cambridge.
William is second in line to the throne after his father, Prince Charles, who is the queen's first-born child. Charles' sister Anne is lower in the line of succession than her younger brothers Andrew and Edward. Charles, in turn, had only sons, William and Harry.
Elizabeth II succeeded her father, King George VI, because he had no sons. If she had had a brother, however much younger he was, he would have jumped above her in the line of succession.
The thorny issue of the succession has been an on-and-off topic in Britain, but has never been resolved. In 2009, then Prime Minister Gordon Brown's government considered a bill that would end the custom of putting males ahead of females in the succession line, as well as lift a ban on British monarchs marrying Roman Catholics. The government did not have time to pursue it before Brown's term ended.
The rule has excluded women from succeeding to the throne in the past. Queen Victoria's first child was a daughter - also called Victoria - but it was her younger brother who succeeded to the throne, as King Edward VII.
Buckingham Palace has always refrained from commenting on the political issue, saying it's a matter for the government to decide.