The BSG is the advisory group to the government on the promotion of broadband services and aims for the UK to be a world-leading broadband-enabled economy by 2010.
Graf, who was the author of the recent independent review of BBC Online, is taking over from Keith Todd CBE, who is stepping down after three years at the helm of the BSG.
Graf explained that the industry faced challenges in making the most of broadband take-up in the UK and pointed out that failure to address them would damage the economy.
"The real challenge now is to make sure that as a nation we leverage the full value of broadband. This is one of the most important issues facing our nation today," he said.
He added: "If we exploit broadband effectively we can improve productivity, innovation, growth and quality of life. But if we fail to keep up with international competitors, we risk becoming a high-cost and low-value economy, it is as simple as that."
Graf was CEO of Trinity from 1993-1999, then CEO of Trinity Mirror until 2003. He is currently working for The Change Partnership and is a director of a number of companies.
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