Mr Bari has publicly condemned the killing of British troops
The BBC has agreed to pay £45,000 in damages to the head of the Muslim Council of Britain over a libellous claim in the Question Time programme.
The claim was made by a panellist on the programme, who accused Muhammad Abdul Bari of implicitly condoning the kidnap and killing of British soldiers.
Mr Bari argued this was untrue, citing his public condemnation of the killing of British troops in Iraq in 2007.
The BBC accepted the argument and apologised unreservedly.
The libellous claim - made on the 12 March 2009 edition of Question Time - came in response to a question from an audience member concerning controversial protests in March by a group of Muslim men against a regiment of British troops on parade in Luton on their return from duty in Iraq.
The audience member asked: "Should these protests we saw last week when the Royal Anglia Regiment came to Luton be banned?"
In response to the question, one of the Question Time panellists suggested that despite having been asked many times to condemn the kidnapping and killing of British soldiers, Mr Bari had failed to do so and thereby implicitly condoned such acts.
The panellist also suggested that Mr Bari believed the kidnapping and killing of British soldiers was a good and Islamic thing.
Mr Bari was not mentioned by name, but was implied in the panellist's reference to the "leadership" of the Muslim Council of Britain.
The BBC is paying £45,000 in damages to Mr Bari - which he will donate to charity - as well as his legal costs.