The British government accepted the couple "were subjected to a harrowing ordeal which caused them significant distress", and said that it had reached "a full and final settlement" with them both.
"Later, during your detention in Libya, we sought information about and from you".
"The UK government has learned many lessons from this period".
"The U.K. government's actions contributed to your detention, rendition and suffering", the letter said. "On behalf of Her Majesty's Government, I apologize unreservedly", PM May wrote in a letter released to the public on May 10.
"We should have understood much sooner the unacceptable practices of some of our worldwide partners".
Under the administration of former President George W. Bush, the Central Intelligence Agency practised so-called "extraordinary renditions", or extra-judicial transfers of suspects from one country to another, in the wake of the September 11, 2001 attacks.
Martha Spurier, director of rights group Liberty, applauded the settlement, but highlighted that many other rendition cases were being ignored.
Following the announcement, which Boudchar attended with her son in London, she thanked the British government for their apology.More news: Gmail's getting an AI-powered Smart Compose feature for faster emailing
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"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".
"A great society does not torture; does not help others to torture; and, when it makes mistakes, it accepts them and apologises".
Belhadj has pursued legal action for years against former British Foreign Secretary Jack Straw, domestic and foreign spy agencies MI5 and MI6, a former intelligence chief and government departments, seeking an apology from all the parties involved.
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.
However, friends of the couple said the United Kingdom had agreed to pay Mr Belhaj and Ms Boudchar's "substantial" legal fees.
The couple have fought a long, high-profile battle with the British Government, claiming part of the deal to reopen diplomatic links with Libya involved the illegal kidnapping and flying of Libyan dissidents to Tripoli. "We accept this was a failing on our part".
Mr Belhaj is now a politician in Libya.