The Premier League club's bid was recommended by the Olympic Park Legacy Company (OPLC) last month, ahead of a rival proposal from north London based Tottenham Hotspur.
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"My colleague the Minister for Sport and the Olympics (Hugh Robertson) and I have today given approval to the recommendation of the OPLC to select the joint bid from West Ham United Football Club and the London Borough of Newham as the preferred bidder for the legacy use of the Olympic Stadium," junior minister Bob Neill said in a statement.
West Ham, whose promise to retain the athletics track in a revamped 60,000-seater stadium was crucial to their successful bid, will now enter negotiations with the OPLC over details such as the length of the lease.
"We are delighted with the progress that has been made and very pleased we have reached this very significant milestone in determining the long term legacy for the Olympic Park following the Games," the statement added.
While the government's and Mayor's support appears to have made West Ham's move to the 500 million pounds stadium a certainty, the relegation threatened club must still satisfy the OPLC that it offers "value for money" to the public sector and will honour its commitments to athletics.
UK Athletics welcomed the government's decision on Thursday but Barry Hearn, chairman of League One football club Leyton Orient, repeated his threat of legal action to try to block West Ham's move.
Orient's current stadium is virtually on the boundary fence of the Olympic Park in East London and Hearn says West Ham's move would breach Premier League rules.
However, the Premier League said on Thursday they would not be reviewing their decision to support West Ham's two-mile relocation from Upton Park to Stratford.
"The Board came to the decision that on balance it would be unreasonable to prevent either Tottenham Hotspur or West Ham United from moving to the Olympic Site as long as they satisfied all of the relevant criteria stipulated by appropriate Olympic and statutory authorities," a statement said.
"It is regrettable that Mr. Hearn is now claiming that Leyton Orient had no input into the Board's decision making process when their views, as expressed in writing at the time by Mr. Hearn, were given due consideration."
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