Father-of-four Shaker Aamer had been detained at the US military jail in Cuba since 2002 without trial.
He was cleared for release at the end of last month, but Mr Aamer’s wife Zin and four children, one of whom he has never met, have been waiting for his return.
His release was confirmed by Foreign Secretary Philip Hammond this morning.
Andy Worthington, co-director of the We Stand With Shaker campaign, said he had informed by Mr Aamer’s lawyer that he is due to return to the UK today.
He said: ‘We’re delighted to hear that his long and unacceptable ordeal has come to an end.
‘We hope he won’t be detained by the British authorities on his return and gets the psychological and medical care that he needs to be able to resume his life with his family in London.’
Other reports suggested he was already on a flight back home.
Human rights charity Reprieve wrote on Twitter: ‘Looks like a plane has left Guantanamo Bay, bound for London.’
But a spokesman for Reprieve said it had no confirmation of Mr Aamer’s release and it would not receive advance warning.
Mr Aamer, 46, says he was working as a charity worker in Afghanistan when he was kidnapped and handed over to US forces in 2001.
During his time in captivity, his lawyers said he was subjected to torture, with beatings and sleep deprivation, and held in solitary confinement for 360 days.
In 2005, he lost half his body weight during a hunger strike.
His family, MPs and actors Mark Rylance and Maxine Peake have also taken part in a 24-hour fast to show their support. Mr Aamer said he cried when he read about the protests.
He was described in US military files obtained by the WikiLeaks website as a ‘close associate of Osama bin Laden’ who fought in the battle of Tora Bora.
However in 2007 the allegations against him were dropped and he was cleared for release.
Despite a formal request by then foreign secretary David Miliband, American authorities refused to allow him to go.
In letters, Mr Aamer said he was not sure if he would know how to respond to his name after being referred to as 239 – his prison number – for more than a decade.
Amnesty International UK director Kate Allen said: ‘After so many twists and turns in this appalling case, we won’t really believe that Shaker Aamer is actually being returned to the UK until his plane touches down on British soil.
‘We should remember what a terrible travesty of justice this case has been, and that having been held in intolerable circumstances for nearly 14 years Mr Aamer will need to time to readjust to his freedom.’
In a letter to Mr Aamer’s US lawyer earlier this month, Clive Stafford Smith, Mr Hammond said he ‘greatly welcomed’ the decision to release his client.
It was claimed Mr Aamer’s release was delayed to appease US politicians visiting the camp.
Three Republican Senators visited the camp on a ‘fact-finding’ mission.
Asked about the timescale, Mr Hammond said: ‘As you know, the US authorities have now informed us that they have decided to return Shaker Aamer to the UK.
‘We greatly welcome this decision. The US government has notified Congress and once that notice period has concluded, Mr Aamer will return to the UK.
‘In the meantime we will continue to work closely with the US administration on arrangements for Mr Aamer’s return.’
Speaking about the delays earlier this week, Mr Stafford Smith, who is also Director of pressure group Reprieve, said: ‘Sadly, as we have said all along, it looks like those who don’t want Shaker released are dragging their feet.
‘We want to thank all those who have been committed to helping Shaker, but we must all continue to press the authorities on both sides of the Atlantic to do as they promised.
‘Surely 14 years of abuse is enough every additional day is an additional insult to justice. He has to come home now, and his family must be put out of their eternal misery.’
Downing Street has refused to comment on the timing of Mr Aamer’s release.
But the PM’s spokesman said earlier this week: ‘We have been working with the US to make sure the case is dealt with as quickly as possible.’