Saudi-born Aamer is alleged to have been a key British-based recruiter and financier for the Al-Qaeda militant network and purportedly worked for Osama Bin Laden in Afghanistan, according to US military documents.
Aamer's lawyer Clive Stafford Smith said that his client, who was captured in Afghanistan in 2001, would probably not be released until the end of next month.
The move comes as President Barack Obama struggles to honour a six-year-old pledge to close the facility before leaving the White House in 2017.
Aamer was captured in Tora Bora in northern Afghanistan in December 2001 before being transferred to Guantanamo in Cuba in February 2002, where he has been held ever since.
Stafford Smith called word of his release "great news, albeit about 13 years too late".
He added: "They only just gave notice to Congress, so that means that without robust intervention, Shaker and his family have to wait until October 25th at the earliest for their reunion."
A US defense official speaking on condition of anonymity said the decision to release him had been taken "taking into consideration the robust security assurances" provided by Britain about how the transfer would take place.
Neither side gave any details of what would happen to Aamer after he returns to Britain.
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