Recently- appointed Carlton president Graham Smorgon said the board decided to increase the number of directors to 10.
"Richard and Adrian bring important skill sets to the Carlton board, both having a successful business background," Smorgon said.
"Adrian is a Carlton premiership player and has continued an involvement with Carlton since retiring as a player and in recent years he has been an active member of the Carlton Blue Suits Coterie Group.
"Richard has been a long time Carlton Social Club member and his outstanding business skills combined with his role as a director of the Carlton Cricket and Football Social Club provide him with a clear understanding of the challenges that the club faces."
Gleeson, who played 176 matches for Carlton from 1986-96 and is a life member of the club, also represented Victoria during his career. Following his retirement, Gleeson established his own business in 1990.
Newton was a director of the Carlton Cricket and Football Social Club from 2002-06 and was also a member of the finance sub-committee. He is the managing director of the Selpam Group of Companies.