They have voted to take up the offer made by Pope Benedict XVI in November that permits vicars and their entire congregations to defect to Rome while keeping many of their Anglican traditions, including married priests.
By issuing the apostolic constitution Anglicanorum coetibus (on groups of Anglicans) the Pope was accused of attempting to poach Anglicans unhappy about decisions taken in their Church to ordain women and sexually-active homosexuals as priests and bishops.
But the Vatican insisted that the move to create self-governing "personal ordinariates", which resemble dioceses in structure, came as a result of requests from at least 30 disaffected Anglican bishops around the world for "corporate reunion" with the Catholic Church.
The Anglican Church in America (ACA) will now enter the Catholic Church as a block, bringing in thousands of converts along with their own bishops, buildings and even a cathedral.
They will worship according to Anglican rubrics, and use the Book of Common Prayer, but they will be in communion with the Pope, recognising him as their leader.
The decision was taken by the House of Bishops of the ACA during a meeting in Orlando, Florida, earlier this week.
The bishops said in a brief statement afterwards that they had agreed to formally "request the implementation of the provisions of the Apostolic Constitution Anglicanorum coetibus in the United States of America by the (Vatican's) Congregation for the Doctrine of the Faith".
The ACA belongs to the Traditional Anglican Communion, which broke from the Anglican Communion nearly 20 years ago because of its drift from orthodox Christian doctrines.
Unlike 77 million Anglicans worldwide, it is not in communion with the much larger US episcopal church nor does it recognise Dr Rowan Williams, the Archbishop of Canterbury, as the head of the church but still considers itself Anglican in its origins.
Its decision to rejoin the Catholic Church represents the second group of Anglican churches to take up the Pope's offer.
The first was the Australian branch of Forward in Faith, a traditionalist group in communion with the Church of England and other mainstream Anglican churches, which last month directed its governing council to take the first steps needed for the mass conversion of 16 parishes to Catholicism.
The UK branch of Forward in Faith is also considering mass conversion but has delayed a decision until July at the earliest – though its leaders are known to be holding secretive meeting with high-ranking Vatican officials.
In the meantime Forward in Faith UK has set up a "Friends of the Ordinariate" group to help to gauge the level of support for conversion among rank-and-file worshippers.
If they decide to take the path to Rome, Britain will see unprecedented numbers of conversions, possibly involving in the region of 200 Anglican congregations, which would amount to thousands of converts.
John Broadhurst, the Anglican Bishop of Fulham and chairman of Forward in Faith, said mass conversion was a real prospect. "We have a thousand priest members in my organisation and there are many others who agree with us," he said last year.
"The main issue for many Anglican priests is now the ownership of parish churches."
In preparation for an influx of converts the Catholic bishops of England and Wales have established a commission which is expected to look at the possibility of church-sharing and also the chances of taking out 100-year leases of some Anglican parishes.
An early conversion came last month, however, when it emerged that Paul Robinson, the former assistant Anglican Bishop of Newcastle, converted just weeks after stepping down from his post.
The 63-year-old was received into the Catholic Church in January and is now a regular worshipper at St George's Roman Catholic Cathedral in Southwark, following a move to London.
'It's really a journey I've been on for some time,' he said. 'It's just like coming home.'
Last summer, Mr Robinson claimed that the dramatic fall in church marriages and baptisms was an indication that Britain was no longer a Christian nation.
He has predicted the demise of the Church of England as the established religion within a generation.
Pope Benedict will visit Britain in September to attend the beatification of Cardinal John Henry Newman, a high-profile Anglican cleric who shocked Victorian England by converting to the Catholic faith.
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