Shaker Aamer arrived back in the UK yesterday after being held for 13 years without charge at the US military facility in Cuba.
It is understood the father of four, who is receiving treatment in hospital, has already been reunited with his wife Zin.
He is due to meet all of his children this weekend, including youngest son Faris, who was born on the same day Mr Aamer arrived at Guantanamo.
Mr Aamer is now expected to bring legal proceedings against the British Government over its alleged complicity in his mistreatment.
The source said: “Proceedings were initiated some years ago on his behalf that could not be followed until his return to the UK.
“They will now, undoubtedly, be progressed.”
Reports that Mr Aamer could be in line for a compensation payout in the region of £1 million were “speculation”, the source added.
Mr Aamer paid an emotional tribute to those who fought for his release after he returned to the UK, saying: “Without their devotion to justice I would not be here in Britain now.”
The 46-year-old arrived on a private plane at Biggin Hill airport in south-east London yesterday afternoon.
In a statement, he 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.
“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.”
Mr Aamer is suffering from post-traumatic stress disorder, one of his lawyers said, as he marks his first full day of freedom back in Britain.
Ramzi Kassem, a law professor at the City University of New York School of Law involved in the case, said Mr Aamer is suffering from a number of medical conditions.
He told BBC Radio 4’s Today programme: “He suffers from a number of conditions both physical and psychological, including post-traumatic stress disorder on the server end of the PTSD spectrum.”
Mr Kassem told Mr Aamer five weeks ago that he was about to be released but said it did not “register” initially.
Mr Aamer later broke out into a huge smile when he realised there was light at the end of the tunnel, the lawyer said.
Former hostage Terry Waite, who was held captive for 1,760 days after going to Beirut in 1987 to negotiate the release of several hostages being held there, urged Mr Aamer to withdraw from public view for a while.
He told Today: “He has suffered a grave injustice. Whatever the background, to keep someone for 13 years without charge is really beyond the pale.”
Mr Waite likened release to deep sea diving, warning “if you come up too quickly you get the bends”.
“If you take it one step at a time and be patient, things could work out in a very good and creative way,” he said.
Mr Waite said Mr Aamer “needs to be very careful” about making any public statements in the near future, warning he may say things he later regrets.
“The best thing is for him to withdraw for a while to get the treatment that’s necessary,” he said.