The 35-year-old has agreed a two-year contract with Aberdeen, bringing to an end a 14-year spell with Celtic.
Brown joined Celtic from Hibernian in 2007 and has won 10 Scottish league titles, six Scottish league Cups and six Scottish Cups.
Brown told Celtic’s website: “It is a huge decision to leave this magnificent club, which has been such a massive part of my life for so long, but this is a new opportunity for me and a new chapter. Celtic will never leave me and the club will forever be in my heart. We still have work to do this season and that will, of course, as ever be my full focus as we try to bring our fans more success.”
Quoted on the Aberdeen website, Brown said: “There is no doubt I had a lot to deliberate when deciding my next steps, particularly after enjoying 14 successful years at Celtic. However, the opportunity to join Aberdeen, a club entering an exciting new period with my former teammate Stephen now at the helm, was one I couldn’t pass up.
“I still feel I have got a lot to give, not only on the pitch, but in a broader capacity as I embark on my coaching journey. I will be relentless in my quest for success for Aberdeen.”
Brown won 55 caps for the Scotland national team.
