Women from Northern Ireland will be able to get free abortions in England, the government has said.
More than 50 MPs from the major parties had backed a Labour-led call for the women to have access to NHS abortions in England. They currently have to pay.
The BBC's political editor said ministers made the concession because it appeared some Tory MPs might back the call, risking a possible defeat.
Northern Ireland's abortion laws are much stricter than the rest of the UK.
Abortions are only allowed in Northern Ireland if a woman's life is at risk or there is a permanent or serious risk to her physical or mental health. Rape, incest and fatal foetal abnormalities are not circumstances in which they can be performed legally.
Women seeking an abortion can travel to England to have one privately, but had not been allowed to have them free on the NHS - a position that was backed by the UK Supreme Court earlier this month.
An amendment on the issue, co-ordinated by Labour's Stella Creasy, which had cross-party backing, had been selected for inclusion in the Queen's Speech debate - which meant Theresa May's government ran the risk of possible defeat.
Since the election Mrs May no longer has a majority of MPs so has to rely on backing from the 10 DUP MPs - but even then she remains vulnerable to a rebellion from her own Conservative MPs.
The news of the change of policy was welcomed by the British Pregnancy Advisory Service which described it as a "landmark moment: for years the women of Northern Ireland, despite being UK citizens and taxpayers, have not been entitled to NHS-funded treatment".
Analysis, by BBC political editor Laura Kuenssberg
Without an overall majority, the Tories were facing a defeat after an impressive campaign by the Labour backbencher Stella Creasy that had garnered support among plenty of Conservatives who looked like they might rebel and vote with her, rather than with their party bosses.
Rather than risk a defeat on a critical day when the Queen's Speech has to pass, Conservative ministers were willing to shift in the end - to make a big concession to avoid being beaten.
Queen's Speech votes are seen as a matter of confidence votes in any government. After chucking away her majority, it is vital today that Theresa May avoids any further embarrassment.
Abortion provider Marie Stopes UK said it was "a hugely positive step forward, but there is no reason why these services shouldn't be provided in Northern Ireland, saving thousands of women each year the cost and stress of travelling to the mainland".
But anti-abortion charity Life said the government should be "neutral on the issue of abortion". "This action by the Department for Women and Equalities not only undermines that neutrality, but also shows an abject disdain for Parliament, by seeking to bring this change in via the back door, avoiding full debate on this issue."
In a debate on the Queen's Speech on Thursday, Ms Creasy said women were having to spend £1,400 to get an abortion in England. Conservative Sir Peter Bottomley asked why, in the case of women from Northern Ireland, "only the poor should be denied lawful abortions".
Chancellor Philip Hammond replied that Justine Greening, the minister for women and equalities, "intends to intervene to fund abortions in England for women arriving here from Northern Ireland".
He later said: "We will be funding [the Government Equalities Office] with additional funding so that she can make a grant to the external organisations that provide these services".
Analysis: James Gallagher, health and science reporter, BBC News
Secrecy and stigma surround women from Northern Ireland deciding to have an abortion.
They will, effectively, be left with two choices - ordering abortion pills online or travelling across the Irish Sea, often to Liverpool.
Online pills are illegal and taken without medical supervision. Going to England comes with the expense of the journey, accommodation, time off work and the procedure itself.
About 700 women came to England, from Northern Ireland, for an abortion last year.
The cost is thought to stop some women from the poorest Northern Ireland families having an abortion in England.
So, the announcement that the procedure, but not the other costs, will be free in England could influence some of those difficult, personal decisions.
But this does not change the culture or visceral debate around abortion in Northern Ireland.
The courts have ruled any decision on abortion law lies with the Northern Ireland Assembly, so any change in the law is deeply unlikely.
Campaigner Sarah Ewart, who travelled to England for a termination in 2013 after doctors said her unborn child had no chance of survival outside the womb, said of the chancellor's announcement that it was positive news, but it was unfortunate that women from Northern Ireland found themselves in this position in the first place.
The prime minister's official spokeswoman said later the government had estimated the cost of the decision to be "around £1m a year" and that the government was "prepared to fund in excess of this" if needed. The estimate was based on the 724 women who travelled from Northern Ireland last year to have an abortion.
She added that ministers had "had concerns about the issue and that's why we're taking action".
Following the concession from the government, Stella Creasy's amendment was withdrawn.
Liberal Democrat deputy leader Jo Swinson congratulated the Labour MP and said: "I'm glad that Justine Greening has acted on this issue, but it is embarrassing that the health secretary had done nothing on this so far and only the threat of a defeat prompted change.
"Women deserve better than having their rights reliant on House of Commons arithmetic."
The concession on abortion came on the same day Belfast's Court of Appeal ruled abortion law in Northern Ireland should be left to the Stormont Assembly, not judges - effectively overturning an earlier ruling that the current abortion laws were incompatible with human rights laws.