The hunt will now begin for a contractor to carry out £150m of conversion work at the 2012 stadium to include retractable seating.
The corporation said “negotiations should be held with the club on final commercial terms for them to move to the stadium.”
The deal will be conditional on final stadium designs and funding terms for converting the venue.
West Ham will reconfigure the ground to provide a retractable/moveable seating solution so the stadium can host football and athletics..
The corporation is also progressing a “non-football” option if financial negotiations with West Ham break down.
It will also start procurement of a contractor to undertake agreed adaptations and is exploring the feasibility of opening the stadium for events in summer 2013 before the adaptation works get underway.
London Mayor Boris Johnson said: “My position on the future of the stadium remains what it has always been: that we can secure a terrific future for this much loved and iconic venue with or without a football team playing there.
“I hope the detailed negotiations with West Ham can succeed, but I am determined that any deal should protect the interests of taxpayers who have paid for the stadium and would have to pay more for adaptations to make it suitable for football.
West Ham vice chairman Karren Brady said: “I guarantee supporters will not be disappointed when our full vision for a Stadium that is world-class in terms of supporter experience, sightlines and facilities is revealed.
“We will seek to share full details as soon as we are able to do so.
“We are now committed to working closely with our new partners and stakeholders in the Stadium to successfully conclude our discussions and bring our collective ambitions to fruition.”
Corporation chief executive Dennis Hone said: “Today’s decision on the stadium represents an important milestone towards reopening the Olympic Stadium.
“If we are to have a football tenant, West Ham and othe parties will need to meet the conditions that the Board has set out today.
“If a deal is not possible then we will bring the stadium back into use as soon as possible. In any event we are exploring options to hold events in summer 2013.”