Prettejohn has been on the L&G board since 2010 and will step down before assuming his new role at the PRA on 10 June.
He is also chairman of Brit Insurance Holdings NV, a position he has held since 2011. He has held a range of other chairman positions including at the Financial Services Practitioner Panel, the Britten-Pears Foundation and the Royal Northern College of Music.
The appointment has been approved by the Chancellor of the Exchequer.
The board already consists of the Governor of the Bank (as Chairman), the deputy governor for financial stability, deputy governor for prudential regulation, chief executive of the FCA and other independent directors, who by law must form a majority of the board.
Independent directors Isain Cornish, Rosalind Gilmore and Charles Randell were appointed in March, and the bank said it would appoint additional board members with insurance industry experience in due course.