The Olympic Park Legacy Company (OPLC), set up to handle the post-Games roles of the various 2012 sites, confirmed that the two Premier League clubs had met Friday's deadline.
Their recommended bid will be announced after a board meeting next Friday with a final decision expected in March.
Tottenham's proposal to demolish the 2012 centrepiece and replace it with a purpose-built football stadium without a running track has attracted strong criticism, particularly from within the world of athletics, but received the backing of Pele in a letter to the OPLC.
"I understand (Tottenham's plans) are based on creating a dedicated football stadium and providing an athletics legacy at the original home of athletics Crystal Palace," he wrote.
"As a player you need to feel the passion and the intensity of the fans. The best stadiums connect the fans to the pitch and if you lose that you lose something that really matters - and eventually you lose the fans."
On Thursday Lamine Diack, president of the International Association of Athletics Federations (IAAF), condemned the club's plan as "outrageous", adding that London's winning 2012 Olympics bid would have been "a lie" if its promise to leave an athletics legacy in the stadium is broken.
West Ham's blueprint, backed by the London borough of Newham, would marry a 60,000-seater football stadium with an athletics track, an option favoured by, among others, London 2012 Organising Committee (LOCOG) chief Sebastian Coe.
West Ham's co-owner David Gold joined players including Scott Parker outside the almost-completed Olympic Stadium, just a couple of miles from the club's Upton Park ground, on Friday to mark the formal launch of the club's bid.
"I think we are the best bid," he told Sky Sports News. "Our bid is not just about money and football, it embraces so many other sports and the community and we believe we will be the proper and rightful winners of this process."
Tottenham chairman Daniel Levy wrote an open letter to the club's fans on the club's website on Friday, outlining the advantages of a move to Stratford rather than pressing on with a new stadium on the site of its current White Hart Lane home.
In it, Levy underlined the club's intention to honour London 2012's legacy promises to the IOC by revamping the Crystal Palace athletics venue in south London but insisted that a new stadium could not house a track.
The OPLC confirmed on Friday that a third option, the original bid idea of stripping the stadium back to a 25,000-seater bowl for athletics and community use, was also on the table, although that is thought to be unsustainable.
