Orient chairman Barry Hearn said West Ham moving into the stadium, just a short distance from Orient's ground, would put the League One club out of business and believes the process whereby West Ham were chosen is flawed.
"We have been notified that Leyton Orient have made the decision to issue proceedings for judicial review," the London Legacy Development Corporation (LLDC) said in a statement.
"Whilst this is disappointing, we believe that our processes have been robust, fair and transparent and that the challenge is misconceived."
Orient, whose attendances rarely top 4,000, were one of the four parties involved in a second bidding process for the Olympic stadium after the initial decision to choose West Ham collapsed under a legal challenge from Tottenham Hotspur.
An announcement confirming West Ham have the green light to move in to a scaled down 60,000-seater stadium is expected in the next few weeks, although Hearn's legal challenge could further delay securing its future use.
Hearn, an outspoken critic of the stadium, said Orient should have been considered for sharing the £430 million stadium with West Ham.
"All parties signed up to the principle of 'teaming' and we don't think that serious consideration has been given to Leyton Orient sharing or 'teaming' with West Ham in the occupancy of the Olympic Stadium," Hearn told the BBC.
"Our legal advice is that there is a fundamental flaw in the LLDC's bidding process that has to be rectified.
"I went to two Queen's Counsels (barristers) to be instructed on this and they both agreed that this whole operation has been a massive mistake by LLDC.
"Those are their words, not mine.
"As such we are very confident the judicial review will show us to be correct and the bidding process will have to take into account the teaming principles."
Hearn said Orient's ground is 750 metres from the boundary of the Olympic Park and believes West Ham's ability to offer cheaper tickets in a 60,000-seat stadium would undermine his club's ability to retain its fan-base.
"West Ham moving to the Olympic Park will put a huge amount of pressure on Leyton Orient to survive at all," he said,
"We are 750 yards away (from the Park) trying to compete with Premiership football. We have no chance in the long-term.
"The common sense way out is; why don't we share the ground?"
Any West Ham move into the stadium is unlikely to be before the 2016-17 season, although the venue will be re-opened this summer to host a Diamond League athletics meeting.
It is also to host the 2017 world athletic championships.