He will take over from chief executive of the Intellectual Property Office, John Alty, who has filled the role since Sir Adrian Smith left to become vice-chancellor of the University of London at the end of August.
Sir John will take responsibility for higher education as well as science and innovation, overseeing BIS's knowledge and innovation group.
He will also have oversight of the research councils, the Higher Education Funding Council for England, the Student Loans Company and the Technology Strategy Board, as well as three BIS executive agencies: the UK Space Agency, the IPO and the National Measurement Office.
Times Higher Education understands that the director general role, advertised with a salary of up to £140,000, attracted significant interest from both within the civil service and academia.
Speaking ahead of the appointment, vice-chancellor of the University of Exeter and former president of Universities UK, Steve Smith, said it was essential that the director general have a deep knowledge of higher education and science, and be able to fight for these budgets within Whitehall.
"Some difficult funding decisions are going to be made if a spending review requires a drop in budgets," he said. "I think you've got to have someone who really knows the sector."
Sir John has both an academic background and experience of the research councils, having been vice-chancellor at Cranfield since December 2006 and spending five years before that as chief executive of the Engineering and Physical Sciences Research Council.
The information and communication technologies engineer has also previously held posts at the University of Essex, the University College of North Wales, Bangor and University College London.
Sir John also served as president of the Institution of Electrical Engineers (now the Institution of Engineering and Technology) from 2004-05 and is a Fellow and former member of the Council of the Royal Academy of Engineering.
Universities and science minister David Willetts said Sir John would bring "huge management and academic experience to the post".
"His team is key to our strategy for delivering strong educational institutions, more innovation and a growing economy," he said.
Sir John added: "There is no more important task in the UK today than creating a strong, growing economy based on science, innovation and research. I am looking forward to working on this with colleagues in the group, in the department more widely and beyond."
Cranfield is a postgraduate only institution. Speaking at the Westminster Higher Education Forum on the future of postgraduate education in London on 17 October, Sir John said he believed that changes to undergraduate funding presented a risk to postgraduate education that needed to be dealt with.