Shaker Aamer's lawyer Clive Stafford Smith told the BBC he would sue the US for compensation but did not expect to win as "American law is pretty insane".
"Compensation is not what Shaker's about. What Shaker wants is a simple apology where they say 'we're really sorry we did this - we'll make sure we set rules in place in future so we don't do it to other people's," he said.
A family reunion is understood to have taken place, with Aamer meeting his youngest son for the first time.
His boy was born on the day he arrived at the US military facility in Cuba 14 years ago.
Aamer, 48, who is suffering from post-traumatic stress disorder, was held in Guantanamo over allegations he had led a Taliban unit and had met Al Qaeda leader Osama Bin Laden, but was never charged.
Aamer also wanted the UK government to hold an "open and transparent" inquiry into allegations that the UK was complicit in torture, his lawyer said.
Instead, he wanted people to learn about it so it never happens again.
Aamer is believed to be in line to receive compensation of at least one million pounds from the UK government after deals were made with previous detainees.
British Prime Minister David Cameron has already asked the government's Intelligence and Security Committee to investigate claims of UK complicity in rendition and torture at Guantanamo Bay.
The Guantanamo Bay detention camp is a US military prison established to detain, interrogate top terror suspects and prosecute detainees for war crimes.
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