Kennedy had indicated he would consider his position after the IFA ruling council passed the motion by 29-14 on Monday night.
Through a statement on the Irish FA’s site, Kennedy said: “I have given over 50 years of service to football in Northern Ireland and I have enjoyed every minute. It has been an honour and privilege to represent the Association locally and internationally and I would like to wish the Irish FA all the best in the years ahead.”
Sports minister Nelson McCausland had said that £23m earmarked for football in Northern Ireland would not be handed over while Kennedy remained president after Kennedy was involved in an unfair dismissal claim regarding chief executive Howard Wells which cost the IFA £500,000.
A replacement has yet to be announced.