The current head of Barclays Capital has previously faced censure from the political world over the amount of remuneration he receives in the investment banking role.
Last year, Mr Diamond took home more than Â£40 million, which was partly made up by the sale of his stake in Barclays' asset management unit BGI, reports the Financial Times.
Business secretary Vince Cable, who wants to split up the banking sector into investment and retail arms, is reportedly angry at Mr Diamond's ascension to the chief executive role.
A source close to the Liberal Democrat minister in the coalition government said: "Vince thinks this shows a lack of awareness about how the public feels. People can't get their head around the sums that Bob Diamond earns."
Liberal Democrat Treasury spokesman Matthew Oakeshott said the appointment was an "extraordinary decision" by Barclays, given Mr Diamond's lack of retail banking experience.
"We have pledged to tackle unacceptable bonuses and to reduce risk: 'Bonus' Bob Diamond personifies both of those things," he added.
Conservative chancellor George Osborne has previously attacked Mr Diamond, telling voters during the election campaign that the remuneration enjoyed by the Barclays executive following the financial crisis "beggared belief".
But despite the protests of the Liberal Democrats about Mr Diamond's promotion, the Treasury and Downing Street have declined to comment on the appointment, labelling it as a matter for the bank.
From the start of October, Mr Diamond will take on more responsibility at the financial institution, becoming president and deputy group chief executive.
He will then start in the top position from March 31st when he replaces outgoing chief executive John Varley, who is to remain at the firm after that date until September 2011 in an advisory capacity on regulatory matters.
By Tony Aynsley