The probe has been launched after it was revealed the original £272 million cost of the conversion has now risen by £51 million to £323 million.
Deputy Mayor Jules Pipe told Sky News: "Last year the previous administration told the public that the costs had risen in total to around £270m. The new Mayor has now been told that cost will be over £320m.
"Understandably, Sadiq has ordered an investigation as to why those two figures are so wildly different.
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"As the new administration at City Hall clearing up the mess of the previous administration, we need to make sure that the stadium runs on a sustainable basis and it is affordable to London."
Campaigners have welcomed the news of an investigation into the projects rising costs.
In a statement, the Olympic Stadium Coalition said: "This is a breakthrough in our long campaign to highlight the intolerable burden on taxpayers of the rebuilding of the Olympic Stadium to the specification of a well off Premier League football club.
"We have never objected to the idea of West Ham playing at the stadium; the question is simply one of how much the club should pay, and how much the taxpayer should be expected to fund.
"Our attempts to seek transparency have been blocked at every turn by the London Legacy Development Corporation and Newham Council. It took two years for us to obtain release of the full rental contract under Freedom of Information law. We believe that all taxpayers deserve to be made fully aware of just how much we are all paying, and how much West Ham United are paying towards both capital and operating costs."
Balfour Beatty were originally awarded the multi-million pound contract to convert the stadium in 2014.
(LM)
