He sent in his resignation to new Indian cricket board chief Sharad Pawar, whose faction ousted Dalmiya's panel in this week's elections.
Dalmiya sent in his resignation to Pawar, who is the agriculture minister in India's Congress-led coalition government, because nominations to the posts are submitted by national cricket boards.
"I had the privilege of being the President of the ACC from 2001-02 and the President of the AACC from 2004-05," Dalmiya wrote in his resignation letter, which was released to the press here.
"In view of the recent changes in the Board of Control for Cricket in India, however, I feel that it is only appropriate that I tender my resignation with immediate effect from both positions," he wrote in the letter.
"Nonetheless, I can assure you of my full support and cooperation as and when required on any matter concerning Indian or international cricket."