Professor Eastwood, who has been head of Birmingham since 2009, will take over at the beginning of September from the current chair, University of Leeds vice-chancellor Michael Arthur.
“I am honoured to have been chosen to chair the Russell Group at this exciting and challenging time for higher education - and research-intensive universities in particular,” said Professor Eastwood.
“The UK boasts world-class universities in terms of reputation, quality, and impact. They play a key role in educating both undergraduate and postgraduate students, carrying out ground-breaking research and developing innovative products and spin-out companies.
“In my term as Russell Group chair I am determined to help ensure that they are able to continue to succeed on a global stage.”
Before his role at Birmingham, Professor Eastwood was chief executive of the Higher Education Funding Council for England, a post he had held since September 2006.
Other former posts have included vice-chancellor of the University of East Anglia, and chief executive of the Arts and Humanities Research Board.
He was also a panel member on the 2010 Browne Review, which paved the way for the government to increase the tuition fee cap in England to £9,000.