Bishop Hind said he would be "happy" to be reordained as a Catholic priest and said that divisions in Anglicanism could make it impossible to stay in the church.
He is the most senior Anglican to admit that he is prepared to accept the offer from the Pope, who shocked the Church of England last week when he paved the way for clergy to convert to Catholicism in large numbers.
The Rt Rev John Broadhurst, the Bishop of Fulham, even claimed that "the Anglican experiment is over". He said it has been shown to be powerless to cope with the crises over gays and women bishops.
In one of the most significant developments since the Reformation, the Pope last week announced that a new structure would be set up to allow disaffected Anglicans to enter full communion with Rome, while maintaining parts of their Protestant heritage.
The move comes after secret talks between the Vatican and a group of senior Anglican bishops. Dr Rowan Williams, the Archbishop of Canterbury, was not informed of the meetings and his advisers even denied that they had taken place when the Sunday Telegraph broke the story last year.
Now Bishop Hind, the most senior traditionalist in the Church of England, has confirmed that he is willing to sacrifice his salary and palace residence to defect to the Catholic Church.
"This is a remarkable new step from the Vatican," he said. "At long last there are some choices for Catholics in the Church of England. I'd be happy to be reordained into the Catholic Church."
While the bishop stressed that this would depend on his previous ministry being recognised, he said that the divisions in the Anglican Communion could make it impossible to stay.
"How can the Church exist if bishops are not in full communion with each other," he said.
Conservative archbishops and bishops have broken ties with their liberal counterparts following the US Episcopal Church's consecration of Gene Robinson, the first openly gay bishop.
Bishop Broadhurst said that the Pope has made his offer in response to the pleas of Anglicans who despair at the disintegration of their Church.
"Anglicanism has become a joke because it has singularly failed to deal with any of its contentious issues," said the bishop, who is chairman of Forward in Faith, the Anglo-Catholic network that represents around 1,000 traditionalist priests.
"There is widespread dissent across the [Anglican] Communion. We are divided in major ways on major issues and the Communion has unravelled.
"I believed in the Church I joined, but it has been revealed to have no doctrine of its own.
"I personally think it has gone past the point of no return. The Anglican experiment is over."
The Rt Rev Martyn Jarrett, the Bishop of Beverley, also said there were questions over the church's survival, adding that the Church of England has changed too dramatically for some traditionalists.
"They are beginning to reflect that the theological position of the Church isn't what they believe," he said.
"The offer from the Vatican is momentous and I felt a great sense of gratitude that the Roman Catholic Church is thinking about the position of traditionalist Anglicans."
Clergy at the Forward in Faith conference, which met in Westminster yesterday, expressed relief that the Pope had provided them with an escape route.
Fr Ed Tomlinson, vicar of St Barnabas, Tunbridge Wells, said that he would be following the lead of Bishop Hind.
"The ship of Anglicanism seems to be going down," he said. "We should be grateful that a lifeboat has been sent.
"I shall be seeking to move to Rome. To stay in the Church of England would be suicide."
Hundreds of traditionalist clergy could join the exodus, though most are waiting for the exact details of the new apostolic constitution to be published.
Battles lie ahead over whether priests who leave to join the Catholic Church will be allowed to take their churches with them, but some bishops have already warned against property seizure.
Dr Williams was only informed of the details of the Pope's decree last weekend and is understood to have been "implacably opposed" to the move.
Lord Carey, the former Archbishop of Canterbury, said he was "appalled" that his successor was given such short notice and was excluded from discussions on the issue.
The Rt Rev Gregory Cameron, Bishop of St Asaph and a close colleague of Dr Williams, said that the archbishop was likely to be saddened by the developments.
"Rowan has worked very hard for unity both within the Anglican Communion, and with Rome, and I suspect he may feel that what has happened is little short of a betrayal, not by the Catholic Church, but by some of those in his own ranks."
"He is likely to be saddened that they felt driven to seek such a radical solution and that some of them now feel they have to go."
"Up until now, the Roman Catholic Church has been putting its weight behind Rowan, but now it is appearing to put its weight behind the conservative groups it can most easily win over."
"The danger is that they'll have every disaffected Anglican beating down the pathway to their door and asking for special treatment."
The Sunday Telegraph can disclose that the planning behind last week's announcement began in 2006, when the Pope asked the Congregation for the Doctrine of the Faith to consider how they could invite Anglicans into the Roman Catholic fold.
He had reached out to disillusioned Anglicans three years earlier, when as head of the Congregation, the most powerful of the Vatican's departments and successor to the medieval Inquisition, he wrote a personal letter to Anglicans in America. He reassured them of the Catholic Church's support of their stand against the liberal tide.