London mayor Sadiq Khan has asked for a review of the Garden Bridge project.
The MP for Barking, Margaret Hodge, will examine whether value for money has been achieved from the taxpayers' £60m contribution to the bridge.
Ms Hodge, a former chair of the House of Commons Public Accounts Committee, will also look at whether transparency standards have been met by public bodies.
Mr Khan has said no more taxpayer money should be spent on the bridge.
The mayor said: "I'm clear that since the beginning of the project there hasn't been the necessary standard of transparency and openness around the Garden Bridge.
"Nearly £40m of public money has already been spent and Londoners deserve more information about the decisions that have been made."
Mrs Hodge said she did not have a view on whether the Garden Bridge was "a fantastic idea or a waste of money".
But James Hatts, editor of local news website SE1, believes the mayor's review is overdue.
He said the Garden Bridge Trust had "already burned through £30-40m of public funds" and "there are huge question marks" over the business plan.
"They are relying on corporate events, souvenirs, credit card readers as you walk onto the bridge so that you can give a donation," he said.
"It's really difficult to see that they are going to get £3.5m year on year. Ultimately, the way Boris Johnson and local authorities structured the planning permission and associated agreements for the bridge means there's a chance the public purse will end up meeting ongoing costs."
Analysis: Tom Edwards, BBC London Transport Correspondent
This could be the beginning of the end for the Garden Bridge. It was meant to be a haven on the Thames and while many in the establishment loved it and thought it would be well received, slowly but surely dissent has grown.
Protesters objected to the location of the bridge as it would affect protected views of St Paul's from South Bank and would require the destruction of numerous established trees on the river banks. They also thought taxpayers money could be better spent elsewhere.
Now it seems like this is a slow death by a thousand reviews.
The review by the Garden Bridge Trust, a third investigation of the scheme, could make it harder for the trust to raise all the private money needed for the scheme. So far not all of it has been raised.
The mayor hasn't killed off the bridge just yet but there are those who think he effectively has done in announcing this review.
Lib Dem London Assembly member Caroline Pidgeon called on Mr Khan to state he will not underwrite the maintenance of the Garden Bridge.
"His current stance of providing a permanent taxpayer bailout to pay for the maintenance of the bridge while claiming to never provide any further public funding for the project is utter nonsense and indefensible."
Campaigners also pointed out that by ordering the review at a cost of £25,000 the mayor was already spending taxpayers' money on the Garden Bridge.
The Garden Bridge aims to link Temple with the Southbank.
Garden Bridge funding so far:
- £30m from Transport for London, £20m has been pledged as a loan to be repaid in full
- £30m from central government
- About £37m has been spent so far
- If the project is finished, then not only will the £20m be repaid to TfL, but the Garden Bridge Trust will need to pay about £22m in VAT to the Treasury - leaving an ultimate cost to the taxpayer of £18 million.