The Scottish Premier League club revealed the former Scotland manager had agreed to continue his involvement with the Dons as a non-executive director.
In a statement on the Aberdeen website, Brown said: "Having reflected long and hard on the situation, I felt the time was right for me to step down as manager."
The 72-year-old took over at Pittodrie in December 2010 after leaving Motherwell but he has struggled to achieve lasting success at the club.
Brown, whose assistant Archie Knox will leave the club in the summer, added: "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.
"Archie and I are 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."
Although he led Aberdeen to two semi-finals - they were also in the League Cup semi-finals when he arrived - he could not secure a top-six place in the Scottish Premier League last season after taking them away from relegation trouble in his first campaign.
The announcement came after a goalless draw with Motherwell left Aberdeen languishing in ninth place.
Brown's contract expires in the summer and with no previous sign of the deal being extended, speculation had already begun over a replacement, with Ross County manager Derek Adams believed to be a strong candidate.
Chairman Stewart Milne said: "Craig and Archie have worked tirelessly to turn the club around over the last 27 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.
"When Craig indicated that he would step down I asked him to become a non-executive director and I am delighted to say this will take effect immediately.
"Craig will have input to all areas of the club like any other board member and will be a fantastic ambassador for Aberdeen Football Club."