The news means the Hammers have taken a giant step towards becoming the first tenants of the Olympic Stadium - though some contractual matters still need to be resolved before the deal is confirmed.
Factors such as the final specification for adaptations to the stadium and the funding needed for it still need to be agreed.
To win preferred bidder status, West Ham had to agree to include the construction of retractable seats over the athletics track.
West Ham would be moving two miles from the 35,000-capacity Upton Park to a stadium which will be downsized from 80,000 seats at the Olympics to 60,000.
A football business college and a group hoping to stage Formula One races were also in the running to take over as the stadium's tenants.
Mayor of London Boris Johnson revealed the news following a meeting of the LDDC, and he warned that if a deal cannot be thrashed out with the Hammers, other options remain.
"Four good bids came in but the top bid was West Ham. There are a lot of negotiations still to go on between the LDDC and West Ham about the terms of the deal," he said.
"If we can't do a deal that protects taxpayer value and the Olympic investment of £9b then that's fine and the stadium will have a fantastic future.
"We are confident there is plenty of time to get the negotiations underway and were we to go with plan B - lots of cultural events and lots of sporting events, lots of operators coming forward - we can get all that going too.
"There's no deal-breaker with West Ham as such - but we are dealing with a public asset worth half a billion pounds and it is my job is to get the best possible deal for the taxpayer."
West Ham United's joint chairmen David Sullivan and David Gold issued a joint statement, saying: ''We believe that this move, together with the realisation of other key goals that the Board set out to achieve from the outset, will play a huge part in helping to realise our ambitious vision to move the club to the next level on behalf of our fantastic and deserving fans."
"Our absolute priority is to take them with us, as well as enticing those supporters that have previously eluded us due to barriers such as affordability and accessibility."
The statement continued: "We also wish to extend our social inclusion agenda to encourage greater community cohesion and expand our equalities and diversity work to make both West Ham and football as a whole more accessible to key target groups.
"We realised our lifelong ambition upon becoming Chairmen of the club we both so passionately support. We are dedicated to West Ham United and the Stadium for the long haul.
"We are now committed to working with the LLDC in full consultation with our supporters to finalise our plans to make the Stadium our home."
West Ham's vice-chairman Karren Brady added: "For the last three years it has been my firm, unwavering belief that the Stadium can truly become a multi-use destination of which east London and the nation as a whole can be proud.
"I have never lost sight of our vision to play our part, along with the Stadium's major stakeholders, in ensuring it grows into a global asset. It is the 'jewel in the crown' of the Park, watched by the world.
"Our vision for the Stadium has always been about standing up for the promises made for London back in Singapore in 2005. We are committed to delivering our promises as set out in our bid.
"The hard work really does start here and work is already well underway to ensure that we really bring our community, which includes 500,000 supporters in east London and Essex alone, with us.
"We are already working with key strategic partners to ensure that unemployed east Londoners in key target groups will have access to sustainable employment in the Olympic Park via the 700-plus job opportunities that West Ham's tenancy will create.
"We guarantee millions of visitors and customers, which will galvanise the Park and act as the catalyst to spark a thriving economy in this part of east London.
"In selecting West Ham United, the LLDC have secured a long-term viable financial future for the Park. On behalf of West Ham United, I feel privileged to have been granted the responsibility to play a key part in delivering a true Games legacy."