Belhaj, who became Tripoli's military commander after Libyan leader Moamer Kadhafi was ousted in the 2011 revolution, claimed British complicity in the couple's capture by the Central Intelligence Agency and later torture by his regime.
Mr Belhaj says MI6 helped the U.S. kidnap him in Thailand in 2004 to return him and his wife to Libya.
They have spent years pursuing British officials through United Kingdom courts seeking compensation and an apology.
Ms Boudchar, who visited parliament yesterday with son Abderrahim, was pregnant with him at the time and was freed shortly before giving birth. Belhaj has said he will settle for £1, but insists he and his wife also receive an apology.
In an interview with Middle East Eye a year ago, Belhaj said: "If the British government or those involved admit to what has happened and apologise I am happy to end it like that".
Mr Belhaj then spent nearly 7 years in prison, where he claims he was tortured in, and that then UK Foreign Secretary Jack Straw authorised the move.
It said Attorney General Jeremy Wright, the government's top lawyer, would make a statement about the matter in parliament later on Thursday. Welcoming the apology, he said: 'It is a historic day, not just for me and my wife. Mr Belhaj, who is now a politician in Libya, was imprisoned for six years, repeatedly tortured and sentenced to death.
He added: "I think the American administration is acting with arrogance and negativity in particular towards the Muslim world".
"The UK Government's actions contributed to your detention, rendition and suffering". The UK government shared information about you to its global partners. We are profoundly sorry for the ordeal that you both suffered and our role in it. "But by today's settlement I look forward to rebuilding my life with dignity and honour, and living free from the weight of these events with my husband and our five handsome children". "We accept this was a failing on our part".
In an opinion piece in the New York Times, Boudchar said she was chained to a wall and tortured by the Central Intelligence Agency when she was pregnant while being detained at a secret site in Thailand.
Belhaj denied that any links between the group and al-Qaeda existed and said he believed his rendition to Libya was part of a covert deal between former UK Prime Minister Tony Blair and former Libyan President Muammar Gaddafi, who was overthrown and killed in a popular uprising in 2011.
Wright told lawmakers that in the wake of the September 11, 2001 attacks, Britain and its global partners "were suddenly adapting to a completely new type and scale of threat".
"It is also important that we should act in line with our values and in accordance with the rule of law", Wright said in his statement.
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