The deal ends more than 20 years of dithering by the Indian Air Force over buying planes to train new pilots for its mainstay MiG-21 fighter jets, which have been dubbed "flying coffins" due to frequent crashes.
An Indian statement said a memorandum of understanding for the 66 planes was signed by Indian Defence Secretary Ajay Prasad and British High Commissioner to India, Michael Arthur.
Prasad said the deal would be worth roughly $1.46bn, though an Indian defence spokesman earlier valued the sale at $1.63bn.
Arthur said the Indian government and BAe will formally sign an order contract next week in London.
"This deal will lead to deeper and wider mutually beneficial interaction between the industries of the two countries," Arthur said.
"This deal will lead to deeper and wider mutually-beneficial interaction between the industries of the two countries"
British High Commissioner
Arthur said Britain would train the first batch of 75 Indian pilots for the Hawks, which could also be configured for combat.
The statement said BAe would sell and supply 24 Hawk jets and the remaining 42 aircraft would be produced in India by state-owned Hindustan Aeronautical Ltd (HAL) under licence from the British firm.
The delivery will begin 35 months from the signing of the accord with BAe.
The statement also said Britain had pledged not to create hurdles to India's manufacture of the Hawks or its components under the licence.
"The United Kingdom government gives assurance that it would take reasonable steps within international law to avoid unjustified prohibitions placed by other countries on the supply by BAe and other associated British equipment manufacturers," it said.
The United States led an array of sanctions imposed on India after its 1998 nuclear tests, crippling the Indian air force's fleet of Sea King helicopters and hitting licensed local production of spare parts of British-designed Jaguar bombers.
India began looking for jet trainers in 1983 and offers were made by BAe, France's Dassault which offered its Alphajet and Russia with its MiG-AT.
Frequent crashes of MiG-21s flown by new pilots have triggered a national outcry and calls for an intermediate aircraft such as the Hawk to train fliers graduating from propeller-driven planes to supersonic jets.