The deal for a 99-year lease will be announced at a news conference, along with details of the revamped stadium featuring retractable seating.
Adapting the stadium is set to cost £150m and the Hammers are expected to move in from August 2016, but the agreement should beforehand allow the venue to be used for the 2015 Rugby World Cup.
Negotiations between London Legacy Development Corporation (LLDC) and West Ham have been long and tortuous since the club was named preferred bidders in December but it is understood that the Corporation's legal advisers have now finally signed off the finer details.
Under the agreement, West Ham will be given the right to use the stadium for all their matches under a 99-year deal, giving the club long-term security but ensuring they will have no property interest in the facility.
The deal will protect public interest should West Ham's owners sell the club for a large profit on the back of the move to the stadium, with the LLDC guaranteed a significant cut.
The LLDC will have the rights to the income from other events such as music concerts, and there will also be a legacy for athletics with a number of events for that sport maintained.
The retractable seating should allow the stadium to be changed from a football venue - with seats on the running track - to one suitable for athletics or concerts within eight days.
London mayor Boris Johnson is expected at the press conference near the stadium, along with mayor of Newham Sir Robin Wales and LLDC chief executive Dennis Hone.
Leyton Orient chairman Barry Hearn insists he is still seeking a judicial review into the bidding process but Sports minister Hugh Robertson claimed that was not a cause for concern.
"That is one for Boris [Johnson] but I am told that all the legal advice is that the review is likely to fail," he said.
Good deal for West Ham, rubbish one for the government and tax payers. I said all along that Spurs bid was the best for everyone but just from the wrong club. Our bid would have been from outside investment and not the tax payer over and above the pre-planned budget for converting the stadium. I hate this legacy rubbish, the world is a vastly different place than it was when we won the Olympic bid so why should we pander to the IOC when it's not now in the interests of the country, especially when the IOC are so alarmed at the state of athletics in past host cities...not. Glad it's not us there though as it didnt seem right, still, I doont want a new shiny Tottenham stadium either. I quite like our shi!!t little sttadium with restricted views and uneven stands.- dryice