One group, the Traditional Anglican Communion, has made its bid to join the Catholic Church known. The fellowship, which split from the Archbishop of Canterbury in 1990, says it has spread to 41 countries and has 400,000 members, although only about half are regular churchgoers.
According to the Apostolic Constitution, married Anglican clergy can be ordained as Catholic priests but they will not be allowed to become bishops (or cardinals or Pope) in accordance with Catholic Church rules.
Both the Vatican and the British archbishops insisted today that this would not disrupt relations between the two churches and that they will continue to work toward "full corporate unity."
The Church of England -- which later grew into the Anglican Communion -- was formed in 1534 when King Henry VIIi split with the Catholic Church after Pope Clement VII refused to annul his marriage to Catherine of Aragon.
"Throughout the more than 450 years of its history, the question of the reunification of Anglicans and Catholics has never been far from mind," the Vatican said in today's statement.
ABC News' Phoebe Natanson in Rome and the Associated Press contributed to this report.