Burnige, who has been a member of the board for some time now, will replace current chairman Theo Paphitis, who retires at the end of the season after nearly eight years at the helm. Paphitis will remain on the board as a non-executive director.
"I am pleased that Jeff Burnige, who has a long association with and deep knowledge of the club, serving as a director since 1986, is to take on the role of chairman," revealed Paphitis.
"He will, I am certain, continue the progress we have made during the last eight years under my Chairmanship. During that time it has been a privilege and an honour to serve as Chairman, and I would like both to thank all who have supported me and to wish Jeff good luck and every success."
Jeff Burnige added: "I am honoured to be taking on the role and, as a lifelong Millwall fan, I know that every other supporter will understand my feelings. I am taking over from Theo after one of the most successful periods in the Club's history. He will be a hard act to follow, but I am determined to continue his good work and strive for further success."
It was also announced that former Chairman Peter Mead has retired from both Boards and that Reg Burr has retired as a director of the football club.