Brown spent 14 years at Celtic after joining from Hibernian in 2007 and won 10 Scottish league titles, six Scottish league Cups and six Scottish Cups before joining Aberdeen in a player-manager role in the summer of 2021.
Brown left Aberdeen in March to concentrate on building himself as a manager, having made 33 appearances in all competitions this season and scoring two goals.
Brown won 55 caps for the Scotland national team.
Brown told Record Sport: "It's been a very difficult decision to call time on my playing career but I'll be 37 next month and I feel the time is right for me to announce that I'm retiring in order to focus fully on becoming a manager.
"It's the end of one chapter but the start of a new one and I'm excited about what the future might hold.
"Obviously I will cherish some amazing moments from my time and none better than winning so many trophies during my years at Celtic. So I'm delighted that the club is now about to celebrate winning the title back.
"It was always an honour for me going out there as captain, knowing the lads were listening to you in that huddle, with 50,000 fans behind us wanting us to do our best.
"Yes my last season didn't go that well but that's football. You'd take nine out of 10 titles all day long! So I'll just have to take that one on the chin. But you learn lessons from the tough times too and I think everyone at the club took those lessons on board."
