The committee will be key to deciding the future of the BBC as it approaches charter renewal next year.
Mr Norman, MP for Hereford and South Herefordshire, replaces John Whittingdale, who was appointed culture secretary last month.
He has said in Parliament he wants to "support the tradition of public service broadcasting".
The politician includes himself among a number of MPs who "feel very warmly" towards the BBC.
But he has also pledged to examine the BBC's spending in the Midlands - where his constituency is based - amid a vocal campaign for the licence fee to be used to be used more locally.
"There is an issue here. It needs proper public consideration and I have already drawn attention to that in the pitch I have made," Mr Norman told the Birmingham Post.
A director of the Hay Festival, Mr Norman is also a trustee of London performing arts space, the Roundhouse, which was founded by his father.
He also plays trumpet in the parliamentary jazz band.
Conservative MP Jesse Norman has been selected to chair the Culture, Media and Sport Select Committee.