The British and Indian governments will today announce the second phase of the UK-India Education and Research Initiative (UKIERI), originally launched in 2006.
The project takes account of India's aim to increase its student numbers from 13 million to about 40 million by 2020 - which will involve the creation of 800 new universities.
The second phase of UKIERI includes "a five-year strategic plan to transform leadership and management in Indian schools, higher education and further education institutions".
It follows a visit to India by David Cameron last July with a delegation that included David Willetts, the universities and science minister, and a number of British vice-chancellors.
The new phase covers four areas: the leadership programme; supporting "innovation partnerships" involving young academics and researchers from British and Indian universities; "developing skills capacity" in Indian vocational education; and "enhancing mobility of students and qualifications".
Mr Willetts said that India had "incredible ambitions" in higher education.
"It is keen to see its universities, particularly its new universities, partner with British universities," he told Times Higher Education.
"I think the whole basis for our relationship is one of mutual respect, one in which we want British students to study in India as well as Indian students studying in Britain."
He added that the UK could make a "big contribution" to helping India raise enrolments.
A spokesman for the Department for Business, Innovation and Skills said that in addition to the £5 million annual funding from the two governments, the coalition was "anticipating that business will invest".
Paul Marshall, chief executive of the 1994 Group, said the announcement was "an excellent example of what can be achieved when the government and the sector work together with business towards shared strategic aims".