Knight has served as director of News Corporation, the parent company of The Times, since 1991, including roles as chairman of the compensation committee and as a member of the audit committee of the board.
He will resign his position as director of News Corporation at the next annual general meeting on 16 October.
Knight also served as chief executive and editor-in-chief of The Daily Telegraph from 1986 to 1989.
Rupert Murdoch, commenting on the appointment, said: "His experience and insight as a journalist and as an executive will be a huge asset to The Times and The Sunday Times as they face the challenges and seize the opportunities of the future."
In July, Murdoch stepped down from a string of roles connected to his newspaper empire. He stood down from News International Group Limited, News Corp Investments and Times Newspaper Holdings.