The UK government apologised for the illegal rendition of a former Libyan rebel commander back to Libya where he was tortured by the Qaddafi regime.
In her letter, Mrs May said that the UK Government believes their account of the events and told them: "Neither of you should have been treated in this way".
He said as part of an out-of-court settlement, Boudchar would receive 500,000 pounds ($677,000).
Her husband also thanked the prime minister and the attorney general in a letter read in parliament.
Belhaj was held for more than six years and said he was subjected to torture. "Now, at last, justice has been done", he said. "Britain has made a wrong right today, and set an example for other nations to follow".
Belhaj's case, and that of another Libyan dissident Sami al-Saadi, whose family was also abducted and rendered to Libya, had been investigated by British police who accumulated almost 30,000 pages of evidence over a five-year period.
For several years, Mr Belhaj has refused to drop the case, without receiving an apology from the British government, alongside a symbolic payment of £1 from each of the defendants involved.
Attorney General Jeremy Wright read out a letter to the couple from the Prime Minister in the House of Commons, where Mrs Boudchar and the son she was carrying 14 year ago were watching from the public gallery.
Boudchar said the case "has forced me to relive the lowest moments in my life for many years, and at times it has been a real struggle to keep going. But by today's settlement I look forward to rebuilding my life with dignity and honor, and living free from the weight of these events with my husband and our five attractive children". "It is a victory for everyone who opposes injustice, secret detention, and torture", said Crider in a written statement following the announcement. "Britain lost its way when it got mixed up in rendition, but today, by apologising for its part in that dark story, the United Kingdom has stood on the right side of history".
52-year-old Mr Belhaj was previously a leading member of the Libyan Islamic Fighting Group (LIFG), an Islamist group which waged an insurgency against the Gadaffi regime throughout the 1990's, including several assassination attempts on Gadaffi himself.
During that time he says he was routinely tortured and mistreated.
It came as Britain reached a "full and final" settlement over the case.
The co-operation with Gaddafi - toppled in 2011 - was linked to the "deal in the desert" that saw then-PM Tony Blair attempt to rebuild ties with the pariah leader.
He did not receive any compensation in the settlement, which Mr Wright said did not involve any admissions of liability, including concerning allegations against former Foreign Secretary Jack Straw and Sir Mark Allen, former head of counter-terrorism at MI6.
However, the truth was revealed, with extraordinary irony, in 2011 when North Atlantic Treaty Organisation aircraft destroyed the offices of Gaddafi's intelligence chief, Moussa Koussa.