He will relinquish his current duties as chairman of the Press Standards Board of Finance, the body that funds the Press Complaints Commission, and chairman of the Broadband Stakeholder Group when he takes up his role on January 1.
His new role will also see him chair the Ofcom Content Board, which has delegated responsibility for the regulation of television and radio quality and standards.
He said he was looking forward to the challenges ahead.
He added: “The communications markets are critically important for the UK economy as a whole, and effective regulation can make a real difference.”
Philip Graf joined the Liverpool Daily Post and Echo in 1983, which became Trinity International Holdings in 1985, subsequently becoming chief executive in 1993.
He became chief executive of Trinity Mirror Group when the company merged with the Mirror Group in 1999, a position he held until September 2002.
In 2003 he was asked by the Secretary of State for Culture, Media and Sport to carry out a review of the BBC’s online activities.
He is a partner with the executive coaching firm Praesta and a trustee of the homelessness charity Crisis.
He received a CBE for services to regional newspapers in the Queen’s birthday honours in 2003.