The agreement has been passed to the US Congress for approval, but if no US lawmaker raises an objection the contract is expected to go ahead.
Boeing and Indian partner Tata have begun to produce Apache fuselages at a plant in India, but today's approval concerns a direct sale of finished products from US manufacturers.
In addition to aircraft, the contract includes night vision sensors, GPS guidance and hundreds of Hellfire anti-armour and Stinger air-to-air missiles.
"This support for the AH-64E will provide an increase in India's defencive capability to counter ground-armoured threats and modernise its armed forces," the US Defence Security Cooperation Agency said, in a statement.
"India will have no difficulty absorbing the helicopters and support equipment into its armed forces. The proposed sale of this equipment and support will not alter the basic military balance in the region.