The former Scotland boss has decided to call time on his career following a three-year stint with the Scottish Premier League outfit, along with right-hand man Archie Knox.
"Having reflected long and hard on the situation, I felt the time was right for me to step down as manager," Brown told the club's official website. "I feel it is important this is out in the public domain as I do not want anything to distract from the playing side over the next few weeks.
"[We're] determined to do whatever we can to help the team finish 2012-13 on a high and we strongly believe we will be leaving a solid base for the next management team to build on."
Chairman Stewart Milne added: "Craig and Archie have worked tirelessly to turn the club around over the last twenty-seven months. They are very much a team, as everyone is aware, and the contribution they have made in taking the club forward is immense. The staff throughout the club hold them in such high regard and they will certainly be a difficult act to follow."
Brown will remain at the club as a non-executive director.