Downing Street has said there will be no exemption from anti-discrimination laws for Catholic adoption agencies.
But Tony Blair said they would get 21 months to prepare for change, calling this a "sensible compromise".
Adoption agencies had warned they would close rather than place children with gay couples, saying that went against their beliefs.
The Catholic Church in England and Wales said it was "deeply disappointed" that no exemption had been offered.
The proposed measures are likely to face a vote in Parliament next month before coming into effect on 6 April.
Mr Blair said he believed ministers had found a "way through" to prevent discrimination and protect the interests of children, which all "reasonable people" should be able to accept.
"There is no place in our society for discrimination. That's why I support the right of gay couples to apply to adopt like any other couple.
"And that way there can be no exemptions for faith-based adoption agencies offering public funded services from regulations that prevent discrimination."
Education Secretary Alan Johnson and Labour MP Angela Eagle, who had both opposed an exemption, welcomed the announcement.
He added: "It's a difficult situation but I think we have found the right balance and a sensible compromise."
If the plan is approved, religious agencies will have a "statutory duty" to refer gay couples to other agencies until the end of 2008.
The government hopes the extra time will allow expertise and knowledge to be passed onto the secular sector, rather than being lost altogether.
Cardinal Cormac Murphy-O'Connor, head of Catholics in England and Wales, said: "It is clear from the prime minister's statement that he has listened to some of the concerns of the Catholic Church in regard to its adoption agencies.
"We are, of course, deeply disappointed that no exemption will be granted to our agencies on the grounds of widely held religious conviction and conscience."
He added: "We note and welcome, however, the government's expressed desire that the experience and excellent work of our agencies is not lost, especially for the benefit of needy children."
Cardinal Murphy-O'Connor also said: "This debate has raised crucial issues for the common good of our society.
"We believe there is an urgent task to reach a new consensus on how best the public role of religious organisations can be safeguarded and their rights upheld."
The Equality Act, due to come into effect in England, Wales and Scotland in April, outlaws discrimination in the provision of goods, facilities and services on the basis of sexual orientation.
Gay groups and some MPs had argued that there could be no exemption on faith grounds.
The row was said to have split the Cabinet.
Communities Secretary Ruth Kelly said government was about "robust debate and finding solutions that meet our principles".
She described the announcement as a "breakthrough" on what had been an "extremely complex issue".
For the Lib Dems, Lorely Burt said a transition period of almost two years seemed "unnecessarily long".
"The wishes of Catholic adoption agencies should not be elevated above the rest of society," she said.
Earlier Conservative leader David Cameron said he would vote for the regulations, if a compromise could not be reached.
He has promised Tory MPs a free vote on what he see as an issue of conscience.