Liverpool striker Luis Suarez has signed a new long-term contract with the club.
Malky Mackay looks set to take charge of Cardiff for the last time at Liverpool on Saturday.
The club revealed he 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 Clydesdale Bank Premier League last season after taking them away from relegation trouble in his first campaign.
And the announcement comes after a goalless draw with Motherwell on Saturday left Aberdeen in ninth place with three games left to the split.
The Dons are two points behind sixth-placed Hibernian but face Celtic at Parkhead on Saturday and look destined to finish in the bottom six for a fourth consecutive season since Jimmy Calderwood lost his job on the day he led the club into Europe.
The club revealed that Brown, who replaced Mark McGhee as manager, would help with their immediate search for his successor.
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.
"He has held a board position at Clyde FC in the past so is well aware of the challenges football faces everywhere as well as here at Aberdeen.
"As a board member he will play a full role like the rest of the board in choosing his successor.
"Archie will always be welcome back at Pittodrie where he has contributed so much over the last couple of years and during that unforgettable period in the 80s along with Sir Alex Ferguson."
Former Scotland manager Brown added: "I have been in football all my life and the opportunity to join the board at Aberdeen FC is a great honour and one that I will contribute to at all levels going forward.
"It was clear to me that the club was keen for me to remain here and I have a burning desire to see this great club back at the very top of the Scottish game where it belongs.
"Everyone, from the board, players, staff and fans, has made me feel so welcome and I'm delighted to remain part of the club going forward."