The Charity Commission has criticised George Galloway and other Mariam Appeal trustees for failing to make sufficient inquiries into the source of donations.
George Galloway set up the Mariam Appeal in 1998
It found the appeal had received significant donations connected with improper transactions made under the Iraqi oil-for-food programme.
It said they had not been sufficiently vigilant but that all the appeal's money was spent on humanitarian aid.
Respect MP Mr Galloway said the allegations were "palpably false".
The Mariam Appeal was set up by Mr Galloway in 1998 to provide medicine and medical help to Iraqis during the last years of Saddam Hussein's rule and under international sanctions.
The oil-for-food programme was set up by the UN to enable Iraq to sell its oil to the world market in the period of the sanctions.
All money raised had to be paid into a UN-controlled account with the funds available to the Iraqi government only for humanitarian purposes and others permitted by the UN Security Council.
In its conclusions, published on its website, the commission says the appeal's known total income, from its inception in 1998 until it ceased operating in early 2003, was just under £1,468,000.
It says the appeal received at least $376,000 (£230,000) in improper donations.
It maintains Jordanian businessman Fawaz Zureikat, who became chairman of the appeal in mid-2001, donated the money to the appeal using cash he had received from oil-for-food contracts.
The commission states: "As Mr Zureikat made his donations to the appeal from commissions and other payments derived from the programme, the commission has concluded that these donations came from improper sources."
The commission found that the appeal trustees "did not make sufficient further enquiries as to the source of the funding" Mr Zureikat was providing.
It concludes the trustees "did not properly discharge their duty of care".
The commission also says that Mr Galloway may have known of the connection between the appeal and the oil-for-food programme.
Andrew Hind, the commission's chief executive, said: "The trustees didn't ask any questions about where the money came from and we have concluded they didn't discharge their legal duties regarding these donations."
'Sloppy and misleading'
He added: "This is an issue as much as anything else about public trust and confidence in charities. It's not acceptable for charities to receive funds from improper sources."
Mr Hind said it was for "other agencies" to decide whether the transactions were illegal under national or international law.
The Charity Commission is a civil regulator and does not have any powers of criminal prosecution.
Mr Galloway and two other trustees - Sabah al-Muktar and Stuart Halford - deny any wrongdoing.
Mr Galloway called the report "sloppy, misleading and partial".