The League One football club, which wants a ground-share at the £429million venue, has asked for permission for a judicial review of the bid process.
Hearn said: "The rules of the bidding process created by the London Legacy Development Corporation (LLDC) we do not believe provided for teaming, which is for all parties to share the stadium.
"It is our legal opinion that this is a fundamental flaw of the bidding process.
"We have gone to the High Court to have the decision struck out."
The LLDC board, which is tasked with sorting out the stadium's future, named West Ham as the number one choice to move into the Olympic Stadium in December.
A LLDC spokesman said: "We have been notified that Leyton Orient have made the decision to issue proceedings for judicial review.
"Whilst this is disappointing, we believe that our processes have been robust, fair and transparent and that the challenge is misconceived."
Hearn argues that the process did not allow Leyton Orient to make an effective case for a ground-share.
He said: "We have to protect ourselves. We are doing everything we can to protect Leyton Orient Football Club, which is endangered by West Ham moving to the stadium."
Ground-sharing is something that "lots of clubs" in Europe do, he suggested.
Hearn said he felt "very confident" now the application to kick-start another legal battle over the future of the showpiece venue in Stratford, east London, has been made.
He had no idea how long the matter would take to get to court or to be resolved.
The original deal for West Ham to take over the stadium collapsed in 2011 due to legal challenges from Tottenham and Leyton Orient.
A deal with West Ham would see the club move two miles from their 35,000-capacity stadium at Upton Park.
The LLDC's decision to unanimously rank the Hammers as the preferred bidder means the Barclays Premier League side are in pole position to move into the stadium, but will not be able to take up residency until 2016-17 at the earliest.
The LLDC picked the Hammers as the preferred bidder from a shortlist of four potential anchor tenants, ahead of rivals from Intelligent Transport Services in association with Formula One, UCFB College of Football Business and Leyton Orient.
Final commercial terms had not been decided between the LLDC and West Ham.
In making the announcement, the LLDC had said the deal was not yet done and dusted as it was also working on an alternative use for the 60,000-seater stadium.
An alternative plan for the venue could include a mix of cultural, sporting and community use.
The stadium is to be a multi-use venue which West Ham would rent for 25 days a year on a 99-year lease.
Pop concerts, community use and athletics, including the 2017 World Athletics Championships, are all set to take place there.