By Jill McGivering
Family planning funding was severely curtailed under President Bush
The United States is one of the biggest supporters of family planning programmes worldwide - so this major change to its funding policy will make a huge difference, especially across Africa and others parts of the developing world.
The lifting of the ban will dismay American anti-abortion groups who say taxpayers' dollars should not be used to pay for abortion or to promote it.
But it's being warmly welcomed by many big international family planning networks, including Marie Stopes International and the International Planned Parenthood Federation (IPPF) who can now re-apply for funding for key programmes.
A spokesman for IPPF, Paul Bell, told the BBC that, before the ban was reintroduced by President Bush, the US was one of its biggest donors. The IPPF estimates that it missed out on $100m in funds during the years of the last Bush administration.
Africa, which tends to have less diversified funding than other parts of the developing world, was perhaps the worst affected in that time.
As a result of the ban, Marie Stopes International had to close several programmes, including a family planning centre and outreach programme in Kenya and a project in Ethiopia which, its spokesman says, was actually more focused on HIV and family planning.
IPPF says that its member association in Ghana was just embarking on a new agreement to expand rural outreach services, involving a network of almost 2,000 health workers.
When President Bush reinforced the ban, the organisation lost about $2m in funding overnight. More than 1,000 outreach workers lost their jobs and, it estimates, about 38,000 women lost contraceptive, post-natal and immunisation services.
Mr Obama's move is welcomed by many family planning groups
Critics argue that the inability of doctors to counsel women who want abortions, or to advise them where they can go to get more information or to have the procedure safely, only leads to more unsafe abortions - which is a major cause of maternal death in many parts of the developing world.
The Mexico City policy, which critics have dubbed the global gag rule, was first introduced by President Reagan in 1984, named after the city where it was unveiled at a United Nations conference.
It was repealed by President Clinton - only to be re-instated by President Bush when he came to office. It applies to foreign non-government groups. American groups with overseas programmes and foreign governments are exempt.
This politicisation of family planning aid causes many problems for organisations, especially small projects which don not have alternative sources of funds. Many complain that they are trapped in a cycle of boom or bust - which makes long-term strategic planning very difficult.
"The United States brings a huge amount of money to the table," said IPPF's Paul Bell. "Now programmes that have been dismantled will have to be restarted - and we'll have to go through the bureaucracy of the application process first.
"But there are also issues of absorption. We have to make sure that programmes are not overwhelmed by a sudden influx of money. And everyone is very conscious that in four or eight years' time, it could all be reversed again."