Sir Menzies Campbell, who is a QC, is to chair a panel to examine how the arrangements could be reformed.
The treaty has been criticised as unfair by the families of Britons facing extradition, particularly Janis Sharp, the mother of Gary McKinnon, the autism sufferer wanted by US authorities to answer hacking charges.
An official review by retired judge Sir Scott Baker concluded last month that the Extradition Act was not biased despite the fact nine times as many Britons have been extradited as Americans.
Mr Clegg, who attacked the treaty in opposition, believes his conclusions were “questionable” but fears the Conservatives will accept them and not attempt to reform the act.
He has set up his own review as Lib Dem leader rather than deputy prime minister and it is expected the findings will form a basis for his party’s policy on which to fight the next general election.
However, the move will also allow him to deflect criticism if the Coalition Government fails to act.
A source close to Mr Clegg said “There is a strong view among Liberal Democrats that Baker’s findings are genuinely questionable.
“The fear is that the Conservatives will accept the findings of the Baker Review and nothing will change in the extradition arrangements between Britain and the US.
“Nick made clear his views on the treaty in Opposition and he wants a second opinion.
“Menzies led the charge on this issue when he was Leader and Nick thinks he is the perfect person to head up a Liberal Democrat review of the issue.”
The panel will focus on concerns that it is easier for America to extradite Britons than vice versa because of the level of evidence required.
The US only need to show “reasonable suspicion” that someone is responsible for an offence while Britain must show the equivalent of “probable cause” to bring an American here.
However, in his official review Sir Scott Baker concluded there was no substantial difference between the two and that the arrangements were not in need of reform.
Figures obtained under the Freedom of Information Act show that since the treaty came into force, nine times as many Britons have been extradited as Americans. In all 28 British citizens have been sent to the United States for trial, compared to just three Americans sent to the UK.
The extradition treaty was agreed in haste between Britain and America shortly after the Sept 11, 2001, terrorist attacks on America. It came into force in Britain in 2004 and in America in 2006.
It was intended to ease the extradition of terrorist suspects between Britain and America.
Since becoming deputy prime minister Mr Clegg has been under pressure to reform the act after previously being a fierce critic of it.
In Opposition, he campaigned outside the Home Office with Mrs Sharp, and called on the Labour Government to “tear up the unequal, unfair treaty”.
MPs are due to debate the extradition rules in the House of Commons on Thursday.
Sir Menzies said: “This is an extremely important issue.
“As I said in the House of Commons this week, I disagree with Lord Baker’s conclusions about the standard of proof needed to extradite people between Britain and America and vice versa.
“I am extremely pleased that Nick has given me the opportunity to consider the process by which this wrong may be righted.”
A Home Office spokesman said: “An independent review into the UK’s extradition arrangements was published on 18 October.
“The review panel, led by Sir Scott Baker, made a number of recommendations to the government. We are considering those recommendations carefully and will respond in due course.”
Dominic Grieve, the Attorney General, suggested last week that Mr McKinnon could be tried in Britain rather than face extradition.
He said Sir Scott Baker’s review offered “guidelines only” and added that the Government was considering giving British judges new powers to bar extradition.
Mrs Sharp last night said the Lib Dem review was “fantastic news” and praised Mr Clegg and Mr Grieve for “standing up for the rights of British citizens”.