Brown agreed a pre-contract to join the Pittodrie side as player/coach where he will work as an assistant for ex-Hibernian team-mate Stephen Glass.
It brings an end to a highly decorated career at Celtic Park, which began with a £4.4 million move from Easter Road in the summer of 2007.
Since then Brown has won 10 Scottish titles, six Scottish Cups and six League Cups to go with two PFA Scotland Players’ Player of the Year awards. He captained the side for over a decade, beginning in February 2010.
He said in a statement on Celtic’s website: “It was a privilege to sign for this great club all those years ago and it has been an absolute honour to play for and captain Celtic for so many years.
"I would like to sincerely thank Peter, Dermot and the Celtic board for their tremendous support over so many years. We have always enjoyed a great relationship and always worked closely together to bring our fans as much success as possible.
“I would also like to thank the great Celtic managers I have had the good fortune to work with and also so many team-mates and, of course, the Celtic fans who have given me such phenomenal support and backing over the years.
“I have always given my best to the club and always wanted the best for our fans. We have enjoyed some fantastic moments and success together, dominating the game in Scotland so regularly and enjoying some great European nights.
“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.”