After admitting that Fifa needs a "profound overhaul", the 79-year-old said he would ask the organisation's executive committee to arrange an "extraordinary congress" where the new president will be elected.
The next Fifa congress is not scheduled to take place until May 2016 in Mexico City. However, Blatter admitted that this will "create unnecessary delay" and he will instead ask for a new one at the earliest opportunity.
Following Blatter's statement, Fifa's head of audit and compliance Domenico Scala said: "While the timing will ultimately be up to the executive committee the timing of election likely to be between December and March.”
Scala added: "I am dedicated to be putting into place the conditions for the election of a new president. There will be reforms to how the elections are conducted."
Blatter said he will remain in charge until the next president is announced.
Who could take over?
While there was no official word on who the front runners will be, Prince Ali al-Hussein of Jordan, who was the only rival to Blatter in last week's election, has been installed as odds-on favourite by bookmakers Betfair.
The president of Uefa Michel Platini is also widely expected to be among the favourites (currently 6/1).
David Gill, the former chief executive of Manchester United who rejected the offer to become a Fifa vice president is also 6/1.
Dutch FA president Michael van Praag and former footballer of the year Luis Figo, who both pulled out of the race at short notice, could be other contenders. Jerome Champagne, Greg Dyke and Martin Glenn are currently thought to be outsiders in the race.
What becomes of the 2018 and 2022 World Cups?
FA chairman Greg Dyke, who said he was delighted with the news, said the destination of the next two World Cups could be up for discussion again: "Something has come out of the events of last week that has caused Mr Blatter to resign… He’s gone. Let’s celebrate... this is nothing to do with Mr Blatter being honourable, he hasn’t been honourable in years.
At long last we can sort out Fifa. We can go back to looking at those two World Cups. If I were Qatar right now I wouldn’t be feeling very comfortable.