The decision comes just before a major deadline for resolution with tram contractor Bilfinger Berger.
Several officials from the government agency Transport Scotland have been appointed senior positions at the city council.
Ministers have also agreed to reinstate £72m of government funding they earlier decided to withhold.
Infrastructure Secretary Alex Neil said the government would work in "partnership" with Edinburgh City Council, but still retained powers of veto and "the power to direct", while insisting: "The buck still stops with the city council."
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Mr Neil added: "The Scottish Government did not back the trams project when Parliament voted on it in 2007, and we share the frustration of many people in Edinburgh over the way the scheme has developed since then.
"We made it clear two weeks ago that we were no longer prepared to commit further public money to a route which was not financially viable and which did not deliver the link to the city centre which people rightly expected.”
"The Scottish government has a strong track record, through Transport Scotland, of delivering major projects like the M74 early and under budget and secured significant savings on the three contracts to deliver the new Forth Replacement Crossing."
With completion of the major construction on the trams due in summer 2014 at a cost of £776m, opposition parties said the government's intervention had come years too late.
The project ground to a halt over two years ago, following a dispute over who should pay for additional costs.
(JG/GK)
