Former Archbishop of Canterbury Lord Carey says he will support legislation that would make it legal for terminally ill people in England and Wales to receive help to end their lives.
Lord Carey writes in the Daily Mail that he has dropped his opposition to the Assisted Dying Bill "in the face of the reality of needless suffering".
But the current Archbishop of Canterbury Justin Welby has called the bill "mistaken and dangerous".
Peers will debate the bill on Friday.
Tabled by Labour peer Lord Falconer, the legislation would make it legal for adults in England and Wales to be given assistance ending their own life. It would apply to those with less than six months to live.
Two doctors would have to independently confirm the patient was terminally ill and had reached their own, informed decision to die.
Some 110 peers are already listed to speak when the House of Lords debates the private members bill on Friday.
Insisting it would not be "anti-Christian" to change the law, Lord Carey said the current situation risked "undermining the principle of human concern which should lie at the heart of our society".
He added: "Today we face a central paradox. In strictly observing the sanctity of life, the Church could now actually be promoting anguish and pain, the very opposite of a Christian message of hope."
When Lord Carey was still the Archbishop of Canterbury he was among the opponents of Lord Joffe's Assisting Dying for the Terminally Ill Bill, which was successfully blocked in the House of Lords in 2006.
But in his article in Saturday's Daily Mail Lord Carey said: "The fact is that I have changed my mind. The old philosophical certainties have collapsed in the face of the reality of needless suffering."
He said it was the case of Tony Nicklinson, who had locked-in syndrome and died after being refused the legal right to die , who had had the "deepest influence" on his decision.
Mr Nicklinson's widow Jane, said Lord Carey's switch was "huge".
"I'm amazed actually and thrilled because the Church has always been one of our greatest opponents," she told BBC Radio 5 live.
"Someone shouldn't be forced to stay alive with daily suffering - his life was a living hell."
BBC religious affairs correspondent Robert Pigott
There's been something of a shocked reaction to what Lord Carey said. Let's remember he's a former archbishop. He still has some influence in the Church, especially among the more traditionalist minded Anglicans.
So what he said really will have some consequences. He'll also have some influence presumably in the House of Lords, having argued in the past strongly against similar legislation.
One of the most telling things about what Lord Carey has said is that he now thinks it's not "un-Christian" to allow people to take their own lives when they're suffering at the end of their lives.
It speaks to a body of people, including in the Anglican church, who now feel they can to some extent re-interpret what it is to be Christian, to be Anglican and how to put that into practice in their everyday lives.
To hear that coming from a stalwart defender of biblical truth like Lord Carey is pretty significant.
Lord Falconer told BBC Radio 5 live that Lord Carey "makes the point that it's not anti-Christian to support the change in the law that my bill proposes".
"I believe it reflects the view of almost everyone in the debate that - whatever view you take about the issues - nobody wants people who are properly motivated by compassion to be prosecuted. And he puts those arguments incredibly powerfully."
'Sword of Damocles'
However, the current Archbishop of Canterbury Justin Welby warned Lord Falconer's bill would mean elderly and disabled people coming under pressure to end their lives.
"What sort of society would we be creating if we were to allow this sword of Damocles to hang over the head of every vulnerable, terminally-ill person in the country?" he wrote in the Times.
"It would be very naive to think that many of the elderly people who are abused and neglected each year, as well as many severely disabled individuals, would not be put under pressure to end their lives if assisted suicide were permitted by law.
"It would be equally naive to believe, as the Assisted Dying Bill suggests, that such pressure could be recognised in every instance by doctors given the task of assessing requests for assisted suicide.
"Abuse, coercion and intimidation can be slow instruments in the hands of the unscrupulous, creating pressure on vulnerable people who are encouraged to 'do the decent thing'."
Assisted dying debate
What is the current law on assisted dying around the UK?
The 1961 Suicide Act makes it an offence to encourage or assist a suicide or a suicide attempt in England and Wales. Anyone doing so could face up to 14 years in prison.
The law is almost identical in Northern Ireland. There is no specific law on assisted suicide in Scotland, creating some uncertainty, although in theory someone could be prosecuted under homicide legislation.
Have there been any previous attempts to change the law?
There have already been several attempts to legalise assisted dying, but these have been rejected.
The Commission on Assisted Dying, established and funded by campaigners who have been calling for a change in the law, concluded in 2012 that there was a "strong case" for allowing assisted suicide for people who are terminally ill in England and Wales.
But the medical profession and disability rights groups, among others, argue that the law should not be changed because it is there to protect the vulnerable in society.
What is the situation abroad?
In other countries, such as Belgium, Luxembourg and the Netherlands, legislation has been introduced to allow assisted dying. France is considering a possible introduction of similar legislation, although there is opposition from its medical ethics council.
Campaign group Dignity in Dying predicts that a lot more countries will follow suit.
The Bishop of Carlisle, the Right Reverend James Newcome, said Lord Carey's comments would not influence any vote by bishops in the House of Lords.
"The general synod has debated it and come to a conclusion. That's the position to which we're sticking."
But Lord Carey did received support from Rabbi Jonathan Romain, an inter-faith leader for campaign group Dignity in Dying.
He said the experience in the US state of Oregon - where assisted dying became legal in 1997 - showed "very few people" would use the right to get help to end their lives.
'Criteria not safeguards'
The Church of England said in a statement that its governing body, the General Synod, had passed a motion on the issue in February 2012.
The motion reaffirmed the Church's "support for the current law on assisted suicide as a means of contributing to a just and compassionate society in which vulnerable people are protected".
And Reverend Rose Hudson-Wilkin, who is the Speaker's chaplain in the House of Commons, said having an assisted suicide law would sanitise death.
"I just happen to believe that matters of life and death in that way is not for us to play with. There are lots and lots of vulnerable people out there... you cannot make a law that is going to have a serious impact on a majority of people."
Dr Peter Saunders, chief executive of the Christian Medical Fellowship said he was concerned about vulnerable people being exploited.
"We've got to think about the people who are going to feel a duty to end their lives so as not to be a burden to others.
"I'm worried about the disabled people, the depressed and elderly, who are going to be put at danger by this bill which really just has eligibility criteria and not safeguards."