The jail is being constructed to decongest the Tihar prisons.
A meeting of the Delhi Cabinet presided by Chief Minister Sheila Dikshit approved the long-pending proposal.
The Public Works Department had conceived the project in 2009 and estimated a total cost of Rs 150 crore which has doubled now.
While giving the go ahead to the project, the Cabinet directed PWD to complete the project within the approved cost of Rs 300 crore.