The first stage in the process, a franchising of the operation to a private sector company, will take place in 1996, with a full transfer to the private sector seven years later.
As part of the 'private finance initiative', the Government is also seeking tenders to build an extension of the railway from the Isle of Dogs under the Thames to Lewisham.
Answering a written parliamentary question, Mr Gummer said: 'Through privatisation the Government aims to ensure that the DLR will continue to develop as a highly efficient, customer-oriented and market-driven passenger service to Docklands, with reduced dependence on public subsidy.'
Since its completion in the late 1980s the DLR has suffered a series of breakdowns and has struggled to cope with the numbers of passengers.
It was designed in the early 1980s when plans for the Docklands enterprise zone were focused on light industrial buildings, not the high-density office developments that emerged after the intervention of Olympia & York, the property company of the Canadian Reichmann Brothers.
Ever since it opened, evening and weekend services have been disrupted to enable the line to be upgraded to take more traffic.
The inadequacy of the railway is often cited as a reason for the problems offices in Docklands have had in attracting tenants.