The settlement is much less than the £200 million Vincent Tchenguiz had originally sought. Robert Tchenguiz, whose damages claim is ongoing, is seeking £100 million.
It also brings to a close an embarrassing chapter for the agency during which it was slammed by senior judges for "sheer incompetence".
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The Iranian-born brothers - two of London's most high-profile entrepreneurs renowned for their lavish lifestyles - were arrested in a blaze of publicity in March 2011 in dawn raids at their homes and offices.
But after the brothers challenged the SFO's handling of the case in 2012, the search warrants obtained by the SFO were found to be unlawful. The SFO dropped its probe into the pair.
The SFO said on Friday it had also agreed to pay Vincent Tchenguiz and his business entities reasonable costs, of which a further £3 million will be paid within 21 days. A final figure for costs is yet to be determined.
SFO Director David Green, who took charge of the agency in April 2012, said the fraud office deeply regretted the errors made.
"On behalf of the SFO I apologise to Mr Tchenguiz for what happened to him. The SFO has changed a great deal since March 2011, and I am determined that the mistakes made over three years ago will not be repeated," he said in an SFO statement.
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Vincent Tchenguiz said he was happy to accept the settlement.
"I have maintained my innocence since day one and this settlement and the apology that I have received from the SFO is total vindication for me."
In a separate statement Robert Tchenguiz said: "I intend to continue to pursue this claim through the courts in order to right the wrongs that have been done."