Aamer, the last British resident held at Guantanamo Bay, paid tribute to his supporters, saying: "Without their devotion to justice I would not be here in Britain now."
The 46-year-old, who was held at the US military facility for 13 years, said he thanks Allah first, then his wife, family and lawyers.
Aamer arrived on a private plane at Biggin Hill airport in south-east London on Friday after being imprisoned at the Cuban facility since 2002.
In a statement issued tonight, Aamer said: "The reason I have been strong is because of the support of people so strongly devoted to the truth.
"If I was the fire to be lit to tell the truth, it was the people who protected the fire from the wind.
"My thanks go to Allah first, second to my wife, my family, to my kids and then to my lawyers who did everything they could to carry the word to the world. I feel obliged to every individual who fought for justice not just for me but to bring an end to Guantanamo.
"Without knowing of their fight I might have given up more than once; I am overwhelmed by what people have done by their actions, their thoughts and their prayers and without their devotion to justice I would not be here in Britain now.
"The reality may be that we cannot establish peace but we can establish justice. If there is anything that will bring this world to peace it is to remove injustice," the Press Association reports.
Aamer's British lawyers Irene Nembhard and Gareth Pierce said he is an "extraordinary man who determined for 14 years that he would return to Britain".
They said: "He achieved this by unimaginable, heroic, sustained courage, the strength of his character and of his faith being for years his only resource. He by the grace of God is now home and this is a new beginning."
During his time in captivity, Aamer's 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.
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. 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.