The OPLC decision followed discussions with the Mayor of London and the Government, which made its stance clear through a statement issued by the Department for Culture, Media and Sport.
"The Government and Mayor of London have decided to end the current process to dispose of the Olympic stadium, which has become bogged down in a number of legal and other challenges," read the DCMS statement.
"The stadium will now be retained it as a public asset and the Olympic Park Legacy Company (OPLC) has been asked to start a new process to secure tenants for the stadium."
In a joint statement with Kim Bromley-Derry, chief executive of the London Borough of Newham, Brady said West Ham would look to become a tenant of the stadium when the tendering process was re-opened and maintained football and athletics could co-exist together.
The statement added: "The true legacy of London 2012 will be the creation of jobs and a generation of young people inspired by sport based around a community home for all by 2014.
"We remain committed to help deliver that legacy promise to the people of London and the nation."
Legal challenges by Tottenham and Leyton Orient, plus an anonymous complaint to the European Commission, had led to fears the stadium, which will have a 85,000 capacity during the Olympics but will drop to 60,000 afterwards, could be left empty for years because of court action.
Orient chairman Barry Hearn, who, along with Spurs, claimed that West Ham's reliance on a £40m loan from Newham Council was effectively state aid, said Tuesday's decision was the right one.
"It is a fabulous day for Leyton Orient," he told Radio 5 live, adding that the club would rival West Ham for the tenancy.
"West Ham are not a shoo-in, that's very good because they will be competing with a host of other people who have claims on and plans for the Olympic Stadium.
"We have already thrown our hand into the ring and we are going to be part of the bidding process," he said.
Tottenham have recently signed new plans to redevelop their White Hart Lane Ground in north London but have also expressed an interest in taking over the Olympic Stadium.
"We welcome the OPLC decision to end the current Olympic Stadium bid process," said a Spurs statement.
"We firmly believe that the bid we put forward was, in fact, a realistic sporting solution for the stadium, along with a substantial return to the taxpayer, community programming and athletics provision."
A fund of £35m has already been earmarked under the Olympic Budget to help transform the Olympic Stadium after the Games, with prospective tenants then being asked to bid for the stadium, which would retain the running track.
Any tenants would then pay an annual rent to the OPLC, which early reports suggested could be around £2m.
Olympics minister Robertson says the decision was made to bring ''certainty to the process''
UK Athletics chief Ed Warner said the OPLC's decision was good news for his sport because it would end the uncertainty surrounding Britain's bid for the World Athletics Championships in 2017.
Lack of clarity over the future of the stadium in 2010 forced Britain to scrap a bid for the 2015 World Championships, which were awarded instead to Beijing, hosts of the 2008 Olympics.
"It's fantastic for UK Athletics and it is a bold and decisive move by the legacy company," Warner told BBC Radio 5 live.
"We can now show the IAAF (International Association of Athletics Federations) that we can deliver for them in time for the 2017 World Championships."
Sports Minister Hugh Robertson agreed Tuesday's announcement would improve London's chances of hosting the event.
He told 5 live that Britain could bid with "full confidence" now that the OPLC had brought "certainty" to the whole process.
London mayor Boris Johnson, meanwhile, insisted the stadium would not become a burden to the taxpayer once the Olympics were over.
"I am confident that this decision is the best way to ensure we have certainty over the stadium's future," he said.
"I believe it will also put us in the place where we always intended to be - delivering a lasting sustainable legacy for the stadium backed up by a robust but flexible business plan that provides a very good return to the taxpayer."
The OPLC has set a deadline of 2014 for the new tenants of the stadium to move in.
For that to happen, planning permission must be submitted by March 2012 to ensure work starts immediately after the 2012 Olympics, which run from 27 July to 12 August, and Paralympics, which end on 9 September, have finished.
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