The Olympic Park Legacy Company announced on Friday that a consortium led by Tottenham/AEG and a rival consortium headed by West Ham/Newham Council would go into the final negotiations ahead of a decision in March.
Margaret Ford, chair of the OPLC, said: "We started this process to ensure the very best legacy for the stadium, and we are now at a point where we have selected the two strongest bids.
"We will go forward to start negotiations with the two consortia of Tottenham Hotspur and AEG, and West Ham United and Newham Council.
"The stadium is a vital and vibrant component of the Olympic Park - securing the most appropriate and viable solution is crucial for our long-term aspirations for the future Queen Elizabeth Olympic Park area."
The announcement means disappointment for a bid by the International Stadia Group, the company that masterminded the premium seat scheme at Wembley Stadium.
It will also mean a straight choice between a bid that would keep a running track inside the stadium - West Ham's - and one that would see the track removed - Tottenham's.
UK Athletics and the British Olympic Association have both spoken in favour of keeping the track.
BOA chairman Lord Moynihan said this week: "We want to see an athletics track inside the stadium, there was a commitment made to the IOC and we hope that the process underway will result in the honouring of that commitment.
"And if there is going to be an athletics legacy within the stadium there needs to be a warm-up track outside.
"Athletics being an integral part of the future of the stadium is a commitment that was made to the IOC and one which I am confident and have every reason to believe will continue into the future."