The family of the last British resident held in Guantanamo Bay have pleaded with authorities to confirm when he will be released.
It was confirmed on Friday that Shaker Aamer is to be freed after more than 13 years in detention without charge.
However, the 46-year-old will not leave the military prison in Cuba immediately as the US administration has to give Congress 30 days' notice of his release.
In a statement, Mr Aamer's relatives welcomed the news "tentatively". They said their hopes have been "dashed before", but described Friday as "a good day".
They added: "It is one that has been far too long coming.
"Shaker was cleared for release from Guantanamo in 2007 and has never faced any sort of a trial or been charged with any crime.
"We have been through a terrible ordeal and we ask the British and American governments not to prolong that ordeal any longer and tell us when we can expect our husband, father and son-in-law to walk back into our lives.
"We would like to thank everyone for their support and ask that the press respect our privacy while we process this news."
The US government has formally notified UK authorities that the Saudi national will be returned to Britain, finally bringing an end to a case that had become a cause celebre.
Successive British governments had pressed for his return after he was originally cleared for release in 2007, while Boris Johnson and Jeremy Corbyn were among the prominent MPs who campaigned for his freedom.
Mr Aamer's daughter Johina has expressed her delight that their ordeal is coming to an end, writing on Twitter: "Thank you everyone for all the support. The news hasn't hit yet. We can't believe we might finally see our Dad after 14 years."
A senior US defence official said the decision to return Mr Aamer to the UK had been approved by Defence Secretary Ashton Carter following a "thorough review" of his case and "robust security assurances" from the British Government.
British officials would not comment on the conditions surrounding his release although it is understood he will be subject to monitoring by the security services.
Mr Aamer, who has a wife and four children living in Battersea, south London, has said he was originally seized by bounty hunters while working as a charity worker in Afghanistan in 2001 shortly after the 9/11 attacks.
He was handed over to US forces and in February 2002 he was transferred to Guantanamo Bay and accused of aiding al Qaeda.
During his time in captivity, his lawyers say 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.
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 were dropped and he was cleared for release.
Despite a formal request for his return by then foreign secretary David Miliband, the US authorities refused to allow him to go.