The move follows the resignation of Jan du Plessis from the role back in March. There was understood to be friction between du Plessis and Philip Jansen, BT’s chief executive.
Crozier is said to be the unanimous choice of the board. He will take up the role on December 1, joining the board the month before.
Headquartered in London, BT is the largest provider of fixed-line, broadband and mobile services in the UK, and also offers subscription TV services including BT Sport, which has rights to the UEFA Champions League soccer.
Crozier was at ITV plc between 2010 and 2017. His roles also include advertising agency Saatchi & Saatchi and the Royal Mail.