During a speech in Edinburgh, the Tory leader said Conservative peer Lord Strathclyde, former leader of the House of Lords, would lead the review.
The internal audit found in 2009-10, when disgraced peer Lord Hanningfield was leader, one driver was finishing at 01:00 and starting again at 07:00.
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Alistair Burt said Israel's decision to involve international figures including former Ulster Unionist leader and Tory peer Lord Trimble in the probe should "ensure credibility".
Among those giving evidence have been songwriter Billy Bragg, former peer Tony Benn, Tory Lords leader Lord Strathclyde and film maker Lord Puttnam.
Former Liberal leader and now Lib Dem peer Lord Steel of Aikwood said it was "quite ridiculous" for the government to expect peers to deal with the report stage in the time left available.
The arrest was in connection with an investigation into the peer's expenses during his time as leader of Essex County Council.
BBC: Lord Hanningfield: High Court reserves arrest judgement
Many other tributes have been paid to the Labour peer, with Sandwell's deputy council leader Mahboob Hussain saying he "always had time to listen".
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It is understood there were two meetings on Monday between Culture Secretary Maria Miller, Labour deputy leader Harriet Harman and Lib Dem peer Jim Wallace to pave the way for the leaders' meeting, our correspondent added.
Last month police and the Crown Prosecution Service decided there was insufficient evidence to make a criminal case against the peer over his expenses claims during his time as leader of Essex County Council and closed their files.
The expectation is that it will be chaired by a senior peer - with some Lords gossip pointing to the former Labour Leader of the Lords, Lady Jay.
Unlikely as it may seem, the leader of Labour Party has placed a long dead Tory peer at the heart of his politics.
Appointed a life peer in the House of Lords, she held junior ministerial posts before becoming leader of the upper house of Parliament, a big job with cabinet status, where she earned a reputation as a shrewd political manager.
Speaking on Monday morning, the opposition leader sought to deflect attention from his backing for Lord Archer by blaming the Tory peer for lying.
Resigning, the UUP peer said he had no regrets about making the remarks and claimed Mr Nesbitt's election of as leader had been a "mistake".
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