The midfielder terminated his contract at Pittodrie less than a year into a two-year deal.
Brown confirmed that the opportunities provided to him as a coach under Stephen Glass would no longer be there with new Dons boss Jim Goodwin.
In a message on social media, Brown explained his departure, thanked fans and revealed his next steps.
"Hi all,” he wrote. “Last season, I was given the opportunity by Stephen and the board at Aberdeen Football Club to take the next step in my football career – continuing to play the game that I love whilst gaining hands on coaching experience.
“Unfortunately the season didn’t go as well as we had hoped, and with the managerial change at the club, the opportunity to both play and coach wasn’t there anymore. After speaking with Jim and Aberdeen, we decided it was best for us to part ways.
"Firstly, I would like to thank Stephen and the board for giving me the opportunity and for the incredible support that you have shown me in the short time I spent at your club. To Allan (Russell), Henry (Apaloo) and the rest of the backroom staff I enjoyed working with you and I leave you my best wishes for the future.
"To the players, I have seen the character, the hard work and the determination that you put in day after day on the training pitch and I hope that it brings you, and everyone at the club, success in the future.
"To the fans, I know I was only with you for a short time but thank you for welcoming me to your club, and to your city. The support I received from everyone, from the terraces to meeting you around the city was unbelievable. Thank you! Aberdeen is a huge club and everyone from the board, staff and players are determined to bring you success both on and off the pitch.
"It has been a whirlwind few days and I am going to take some time to consider all my options and relax with my family. I am sure I will get a few rounds of golf in as well.
"Thank you and until we meet again.”
Brown was a candidate for the St Mirren post which Goodwin left to make the move to Aberdeen but Stephen Robinson, the former Motherwell manager, was chosen as the replacement.
His former Celtic boss Brendan Rodgers confirmed an invitation is there for Brown to spend time with him at Premier League side Leicester City.
Meanwhile, current Celtic manager Ange Postecoglou confirmed the door is always open for the former captain.
He said: "From my perspective, I don't think anyone should be in any doubt that there will always be an open door here for Scott Brown.
"The guy is one of the legends of this football club and will go down as one of the greatest ever.”