Mr Aamer 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. But 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."