The MP for Barking, Margaret Hodge, will examine whether value for money has been achieved from the taxpayers' £60m contribution to the bridge.
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.
Khan has said no more taxpayer money should be spent on the bridge.
Khan 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 on the Garden Bridge project, and Londoners deserve far more information about the decisions that have been made around how their money is being spent.
"Margaret Hodge is hugely respected for her work scrutinising some of the UK’s largest and most high-profile publicly funded bodies. There’s no better qualified person to get to the bottom of the procurement process around the Garden Bridge, and establish whether Londoners have been getting value for money since the project began.
"I am absolutely clear that no new London taxpayers’ funds should be committed to the Garden Bridge, but I’m also determined that the Garden Bridge review helps the project achieve higher standards of accountability and transparency it has so far been lacking."
Hodge said: "I’m delighted to accept Sadiq’s offer to look in detail at some of the key decisions made so far around the Garden Bridge. It’s not a project that I have previously had an opinion on either for or against, but given the millions of pounds of public money allocated to the project, it is clear that there needs to be far more transparency around how funds are being spent. The planned bridge is a major project in an iconic part of London, and there are clearly questions that remain unanswered around issues like procurement.
"From his first day in office Sadiq has been relentless in his drive to ensure Londoners get value for money, both around the Garden Bridge and other areas of major spending. I look forward to presenting the findings of the review, and assessing the lessons we can learn for other major projects in our city."
The terms of the reference for the Garden Bridge review will include:
-To assess the public sector contribution to the Garden Bridge project and whether value for money has been achieved.
-To investigate the conduct of Transport for London, the Greater London Authority and other relevant authorities in regard to the Garden Bridge project from first proposal to date.
-To achieve this through assessing the findings of previous reviews, interviewing current and former GLA/TfL staff and other stakeholders, and investigating more deeply as required.
-To set out any lessons that should be learnt in order to improve the conduct of potential and approved projects in the future.
-To produce a report for the Mayor of London, which will be published in full.