The GoM, headed by Finance Minister Pranab Mukherjee, has been asked to report back to the Union Cabinet within 60 days with its recommendations after the January 6 notification.
The eight-member committee was set up last week to suggest measures, including legislative and administrative, to tackle corruption.
The GoM will consider "all measures, legislative and administrative, to tackle corruption and improve transparency", the notification said.
The terms of reference also include state funding of elections, ensuring full transparency in public procurement and contracts and enunciation of a new public procurement policy, relinquishing of discretionary powers enjoyed by the union ministers and introduction of open and competitive system of exploiting natural resources.
The eight-member group includes Ministers P Chidambaram, Sharad Pawar, A K Antony, M Veerappa Moily, Kapil Sibal, Mamata Banerjee and M K Alagiri.
The group has been set up in the backdrop of the five-point plan of action outlined by Congress President Sonia Gandhi last month to tackle corruption "head-on".
Gandhi`s prescription included fast-tracking all cases against public servants including politicians, taking forward the proposal of state-funding of elections, legislative and clear procedures to ensure transparency in public procurement and shedding of discretionary powers by chief ministers and all ministers, including at the Centre.
She had also suggested an open competitive system of exploiting natural resources was also needed.
The government has been facing an onslaught from the Opposition over a series of scams, including those involving 2G spectrum allocation, CWG and Adarsh Housing Society of Mumbai.
The Opposition has been relentlessly pressing for formation of a Joint Parliamentary Committee to probe these scams but the government has resisted it.