He was held in a Libyan jail for nearly 6 years, where he claims he was questioned by United Kingdom officials.
Following a landmark High Court ruling the Prime Minister wrote to Abdel Hakim Balhaj and his wife Fatima Boudchar, who was heavily pregnant when she was detained and tortured, accepting that "the UK Government's actions contributed to your detention, rendition and suffering".
"The best that I think any government can do is to put in place the processes and practices that mean the right values are applied to the judgements that we have to take, including in what are very hard cases". We are profoundly sorry for the ordeal that you both suffered and our role in it.
"During your detention in Libya, we sought information about and from you". We wrongly missed opportunities to alleviate your plight. "We should have understood much sooner the unacceptable practices of some of our worldwide partners and we sincerely regret our failures", the prime minister's statement also said.
Wright also announced that Boudchar would receive £500,000 in compensation for the government's role in the treatment that has been described as appalling.
The apology is the first time that a minister has formally apologised for the actions of Britain's security services in a particular case and represents a remarkable volte face by the Government, which had repeatedly refused to give ground in court proceedings despite the existence of damning documents showing that MI6 had co-operated closely with Colonel Gaddafi's intelligence service.
Mr Wright said that the "unacceptable practices of some of our worldwide partners should have been realised sooner".
He added that he regretted that it had taken so long to resolve the matter. It says that the couple's "harrowing experiences...[are] deeply troubling", and that the UK Government "believes [their] accounts" of their abduction and torture. "It was done in Thailand at the hands of the CIA".
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While the Saadi family received a £2m ($2.5m) settlement two years ago, Belhaj insisted he only wanted an apology and a symbolic £1 ($1.24) payment from each of the defendants.
In 2004, then-British Prime Minister Tony Blair met Gadhafi in Libya, beginning a thaw in relations dubbed the "deal in the desert".
Mr Allen's role in the affair was investigated by the Metropolitan Police, but prosecutors decided not to press charges in June 2016.
Belhaj, a former fighter in the Libyan Islamic Fighting Group that had opposed Gadhafi, and his wife were kidnapped in Thailand in 2004 and sent to Libya.
The 52-year-old dissident, who spent six years in jail in Libya before Gaddafi fell from power in the Arab Spring of 2011, claims he was tortured throughout his imprisonment.
After his release, Belhadj went on to command an Islamist rebel group that helped topple Gaddafi in 2011.
Jack Straw and Sir Mark Allen have denied any wrong-doing. "Neither of you should have been treated in this way", the letter said. For more than six years I have made clear that I had a single goal in bringing this case: justice.
In 1988, amid a regime clamp down, much of the LIFG fled to Afghanistan, where a warrant claims Mr Belhaj formed "close relationships" with senior Al Qaeda members and Taliban chief Mullah Omar.