Dame Margaret Hodge has been found to have breached the MPs' code of conduct, by the Committee on Standards.
The inquiry arose from a complaint about the Labour MP's use of parliamentary facilities for her review of the London Garden Bridge project.
The code states MPs should use public resources only "in support of parliamentary duties".
Dame Margaret said she was "extremely sorry" for "inadvertently" breaching the code.
The inquiry concluded the review had not been carried out as part of Dame Margaret's parliamentary activities, because it had been commissioned by an outside body for its own purposes.
The £200m plan to build a bridge covered with trees over the River Thames was abandoned following Dame Margaret's review, which was published in April.
The review found it would be better to scrap the project rather than risk uncertain costs.
During the review Dame Margaret had held about 20 meetings in her parliamentary office, taking evidence from about 40 people, the committee said.
She had also used some House of Commons stationery and the House-provided telephone service in support of the review.
The inquiry accepted Dame Margaret had not been motivated by financial gain, although she had received a financial benefit.
The committee said Dame Margaret had initially offered to carry out the review on behalf of the Greater London Authority without payment, but after the extent of the work had become apparent she had accepted a payment of £9,500 from the GLA.
The committee recommended Dame Margaret apologised to the House of Commons for the breach on a point of order.
Dame Margaret said: "I am extremely sorry that I inadvertently breached parliamentary rules.
"I carried out this inquiry in good faith and in the public interest.
"I think all MPs would benefit from greater clarity in the rules governing the use of offices."
Conservative member of the London Assembly Andrew Boff, who lodged the complaint which prompted the inquiry, said the verdict left "a sour taste".
He said: "As an MP of over 20 years' experience and a former chair of the Public Accounts Committee it seems hard to believe she was unaware of the rules."