Under his leadership, the group invented and dominated the free newspaper industry. Metro is now the world's biggest international newspaper brand; it has 22.8 million daily readers.
Tornberg, who has worked with the company since its foundation in 1995, is expected to leave by the summer.
He said his experience had been a "truly amazing journey", but felt the time was right to hand over daily leadership of the group.
Dennis Malamatinas, the chairman, said the search for Tornberg's successor would begin immediately. Tornberg is expected to continue working in a non-executive position.