Accepting the post, Miller said: "I am delighted to have been appointed as the culture secretary by the prime minister and am very much looking forward to tackling the many challenges that the role will bring."
Miller, who has been promoted to the cabinet for the first time, will juggle the new position with the role of minister for women and equalities.
She was elected as Conservative MP for Basingstoke in May 2003 and most recently served as minister for disabled people at the Department of Work and Pensions.
Responding to the appointment, Arts Council England chief executive Alan Davey said: "Maria assumes this important post at a time of great opportunities and challenges for arts and culture, as we look to secure the legacy of the hugely successful Cultural Olympiad.
"I look forward to working with her to ensure we maintain the world class cultural offer that is so much a part of who we are as a nation, and that we seize the opportunities provided by the cultural and creative industries to drive economic growth."