Approval for the deal will make millionaires out of many of Porterbrook's 50 staff, led by managing director Sandy Anderson, who will make pounds 36.2m out of his shares in the company.
John Taylor, the corporate and consumer affairs minister, said he had decided not to refer the proposed takeover to the Monopolies and Mergers Commission, provided Stagecoach gave legally-binding undertakings to overcome competition concerns.
The undertakings, which will be policed by of the Office of Fair Trading, are designed to prevent Stagecoach from using Porterbrook to cross-subsidise its passenger rail franchises and discriminating against rival train operators.
The Government sold Porterbrook to a management buyout team backed by Charterhouse Development Capital for pounds 527m only 10 months ago.
Approval for the takeover by Stagecoach is now likely to trigger consolidation among other train operating and train leasing companies. Nomura, which bought one of the other two rolling stock leasing companies, Angel Train Contracts, for pounds 700m has already indicated that it will seek a link-up with a train operator.
The undertakings also require Stagecoach to publish separate accounts for its train operating and rolling stock businesses and not to use information gained from Porterbrook about competitors to help its existing passenger franchises or to aid it when tendering for further franchises.
Stagecoach already runs South West Trains and the Island Line on the Isle of Wight and has been shortlisted for Merseyrail. It also intends to bid for the seven franchises still to be put out to tender.
Keith Cochrane, Stagecoach's finance director, said the undertakings were broadly in line with those the company had offered itself when it announced the bid for Porterbrook in July.
He said the approval would enable Porterbrook to proceed with a pounds 90m order for 30 new trains for South West Trains.