Bazalgette will take on the role on 12 May 2016, when Norman stands down from the role after more than six years at the broadcaster’s annual general meeting.
A non-executive director of ITV since June 2013, Bazalgette resigned as Arts Council England chair last month. He is a former chairman of Endemol UK and the current president of the Royal Television Society.
Andy Haste, the senior independent non-executive director at ITV, said: "We went through an extensive and rigorous process to ensure that we found the best possible candidate to become the next chairman of ITV.
"Out of a strong field of candidates, it was very clear to us that Peter is the right person to take on the role and we're delighted that he has accepted."
ITV will be the third broadcaster to get a new chairman this year. Last month Channel 4 appointed Charles Gurussa, the easyJet deputy chairman, as its chairman, replacing Lord Burns.
Sky also rehired James Murdoch as its chairman in January.