The decision was taken in a meeting chaired by Union Home Minister Rajnath Singh in New Delhi.
"The committee approved the assistance from the National Disaster Relief Fund (NDRF) in respect of Karnataka to the tune of Rs 795.54 crore," a Home Ministry statement said.
The committee examined the proposal based on the report of the inter-ministerial central team which visited the state.
Finance Minister Arun Jaitley and Minister for Agriculture and Farmers' Welfare Radha Mohan Singh also attended the meeting.
Karnataka Chief Minister Siddaramaiah has said the state had suffered a crop loss of Rs 25,000 crore. It asked the Centre for a package of Rs 4,702.54 crore to help tide over the drought.
It is estimated that some 1,000 farmers have committed suicide in Karnataka in the past few years due to crop loss and heavy debts, an official said.