The trust, which took over from the corporation's board of governors on January 1st this year, was created following recommendations in 2004's Hutton Report.
Sir Michael, a former council chief executive, professor of public policy at Birmingham University and the author of last month's Lyons Inquiry into local government, said it was a "great privilege to be appointed".
"As the BBC's sovereign body, our duty is to ensure the public who pay for the BBC retain overall control of their BBC. As chairman I will never lose sight of the public's core expectations of editorial independence and quality programmes across television, radio and the internet which inform, educate and entertain," he insisted.
"I look forward to the exciting challenges of the future and working with my colleagues on the trust to ensure the BBC provides a quality service to justify the public's continuing support."
Broadcasting and entertainment union Bectu has welcomed Sir Michael's appointment, accusing the trust of being "rudderless" over the last three months.
But the union's BBC official Luke Crawley warned that the corporation had a "difficult period ahead, dealing with the below inflation licence fee settlement".
"The new chairman should be under no illusion: Bectu members will not be prepared to have their jobs sacrificed in order to make ends meet. We do not see any reason for large scale redundancies and any proposals for this will be opposed with industrial action," Mr Crawley added.
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