A fall-back option excluding football is also being developed should the deal with West Ham fall through after what has been a lengthy process to find an anchor tenant for the £430 million stadium.
"I hope the detailed negotiations with West Ham can succeed," Johnson said.
"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," he added.
West Ham want to convert the stadium into a 60,000-seater venue with retractable seating to go over the athletics track. Its capacity was 80,000 during this year's Olympics.
Sharing the costs of conversion and ensuring taxpayers stand to benefit from any increase in the value of the club following the move are the main stumbling blocks in the way of a deal.
The Olympic Stadium, centrepiece of the London Games, was funded by public money.
West Ham have played at the Boleyn Ground, often referred to as Upton Park, in East London since 1904.
The club welcomed the decision made by the London Legacy Development Corporation (LLDC), a public body chaired by the mayor.
"We are dedicated to West Ham United and the stadium for the long haul," West Ham co-chairmen David Sullivan and David Gold said in a statement.
"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."
- Sports & Recreation
- West Ham