Sources close to the Premier League club said they were hopeful of "good news" as long-running negotiations on the future of the stadium drew to a close, with confirmation of expected later today in a press conference.
Details of the newly-revamped stadium will also be revealed later.
The club agreed a 99-year lease with the London Legacy Development Corporation in a deal that both parties are now understood to be happy with.
Retractable seating is set to be installed, which would allow the stadium to be changed from a football venue – with seats on the running track – to an arena suitable for athletics events or concerts within eight days.
The club also wants to add a new roof to keep fans dry during the winter and executive boxes.
The stadium had an 80,000 capacity during the Olympics but West Ham plan to cut that to 60,000 for football matches.
The running track will remain and the stadium will host the 2017 world athletics championships.
West Ham were named in December as the preferred bidder to move in, but London mayor Boris Johnson warned that a "Plan B" was being developed in case terms could not be agreed.
Hugh Robertson, the sports minister, refused to confirm the imminent announcement but told the Guardian: "I thought there was a really obvious end to this, which was going to be a multi-use stadium with football at its heart. I always suspected that would be the way to get the stadium best used."
The stadium stands empty at the moment but will host the world's top athletes at a meeting at the end of July to mark the first anniversary of the London Olympics.
London authorities also plan a series of concerts over the summer to bring the stadium back to life and show that it would not be reliant solely on soccer for its future.
One of the stumbling blocks to a deal with West Ham has been who pays a bill of up to 150 million pounds to convert it into a soccer venue.
The London Legacy Development Corporation, the body responsible for the stadium, also wants to ensure that the taxpayer benefits from any increase in value of the club if owners David Gold and David Sullivan were to decide to sell it after the move.
West Ham have played at the Boleyn Ground, better known as Upton Park, in east London since 1904. Around three miles from the Olympic site, the ground is big on atmosphere but can only hold about 35,000 fans.
