Legislation that would allow terminally ill people in England and Wales receive help to end their lives is due to be discussed by peers on Friday.
Lord Carey said he had changed his opinion and no longer thought a change in the law was 'anti Christian'.
He said not changing the current situation would risk "undermining the principle of human concern which should lie at the heart of our society".
The proposals were tabled by Labour peer Lord Falconer and would mean those with less than six months to live could be given assistance to die.
Before any decision could be made two doctors would have to confirm the patient was terminally ill and had reached the decision without any pressure from friends of family.
The current Archbishop of Canterbury Justin Welby has called the proposals "mistaken and dangerous".
Writing in the 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".
The former leader of the Church of England said he had been re-reading scripture and it had made him "less and less certain of my opposition to the right to die".
He said: "Until recently, I would have fiercely opposed Lord Falconer's bill, following the traditional line of the Christian Church. I would have used the time-honoured argument that we should be devoting ourselves to care, not killing.
"I would have paraded all the usual concerns about the risks of 'slippery slopes' and 'state-sponsored euthanasia'.
"But those arguments which persuaded me in the past seem to lack power and authority when confronted with the experiences of those approaching a painful death.
"It fails to address the fundamental question as to why we should force terminally ill patients to an unbearable point. It is the magnitude of suffering that has been preying on my mind as the discussion over the right to die has intensified.
"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".
Lord Carey said he maintained his opposition to assisted suicide which would give anyone help to end their lives, not just the terminally ill.
Writing for The Times the current Archbishop of Canterbury Justin Welby said: "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'".
Several members of the government could back the issue as both houses of Parliament are being given a free vote.