However, the commission has refused to accept the findings and apologise and the Parliamentary Ombudsman is now referring the case to MPs for possible further action.
In 2009, the commission decided after a long-running investigation that the donations received from 5th Avenue Partners, ahead of the 2005 General Election when Charles Kennedy was the LibDem leader, had been permissible and the party should be allowed to keep them.
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5th Avenue Partners was the trading company of Brown, 48, who in 2008 was convicted of fraud in his absence for stealing more than £5m after posing as a bond dealer with royal connections.
He spent nearly four years on the run before starting a seven-year jail sentence in 2012.
Brown, of Glasgow, would not have been able to donate personally as he was not registered to vote and the commission had previously told the party it should have done more to ensure rules barring gifts from foreign firms with no activities in the UK had not been breached.
But the Ombudsman said the Commission "did not make adequate enquiries of the party" and simply "relied on assurances" given by LibDem chiefs that they had indeed taken all reasonable steps at the time to establish the donations were legitimate.
Upholding a complaint of maladministration against the body which oversees elections and party funding, it said the commission "was not able to reach an informed decision on whether or not the rules had been observed".
The ombudsman concluded: "The commission failed to seek relevant evidence at the outset, failed to give an informed view on the matter and failed to review the position on the receipt of new evidence."
Initial checks, it said, "fell significantly short of what was required", regarding cash injections and donated flights.
The commission accepted the flights were paid for by the UK part of 5th Avenue and not its Swiss parent despite having "no credible evidence" that this was the case.
The watchdog said: "It failed to ask for relevant information without good reason and so failed adequately to discharge its monitoring function. That was maladministration.
"The Commission did not follow up the concerns that it had about the robustness of the checks the party had made as it had said it would. That was maladministration.
The report recommended the commission apologise to the individual who had lodged formal complaints about the decision to allow the donation, a constituent of John Stevenson, the Conservative MP for Carlisle, named only as Mr P.
However, it has refused, disputing the findings and agreeing only to set out the lessons that have been learned from the case and to review the adequacy of subsequently published guidance on what constitutes "carrying on a business" and what checks a party should carry out.
At Westminster Labour, given the failings highlighted by the ombudsman, called on the LibDem leader to hand back the money.
Michael Dugher, the Shadow Cabinet Office Minister, said: "Nick Clegg and the Liberal Democrats have justified their inaction against the convicted fraudster Michael Brown by hiding behind a report which has now been totally discredited.
"For years, Clegg has dodged questions on when the LibDems will pay back the donations. He has nowhere now to hide. He should do the decent thing and pay back this money straight away."
Labour backbencher John Mann said he would table a Commons motion calling on the party to repay the money, saying: "They now have no choice but to do this."
But a senior LibDem source made clear this would not happen.
The source said: "This donation was made before Nick Clegg was elected as an MP, let alone became party leader. As the report says, the ombudsman makes no findings about the actions taken by the Liberal Democrats.
"The party fully complied with the regulations set out by the Electoral Commission.
"The Commission inquiry in 2009 found the party accepted the donation in good faith and were in no way at fault and it cleared the party of all wrongdoing and accepted that at the time of the donation 5th Avenue Ltd was a permissible donor."
Were Mr Clegg ever to decide to repay the £2.4m, by law the money would not go back to a convicted fraudster but the so-called Consolidated Fund, the Coalition's bank account.