Professor McGhee will officially take up the role from 1 May, replacing Les Ebdon, who stood down in February after being named the next director of the Office for Fair Access.
A chartered psychologist and a graduate of the universities of Glasgow and Oxford, Professor McGhee was the first from his family to go to university.
He is known as a keen user of social media, and is a prolific tweeter.
“I am delighted and honoured to have been elected as the chair of Million+,” he said. “I would like to pay tribute to the work of Les Ebdon who ensured that Million+ is an important and independent voice for higher education with a strong reputation for analysis and advocacy.
“Governments and politicians need this evidence base if they are to maximise the potential contribution of all students and universities to society and the economy.
“This role will be particularly important over the next few years as we face the challenges of rising to meet the aspirations of millions of students and their families, the opportunities of the global demand for UK higher education and the impact of funding changes on the sector.”
Professor McGhee, who has been vice-chancellor at UEL since February 2010, is a member of the Higher Education Funding Council for England’s committee on teaching, quality and the student experience.