The plan requires International Gymnastics Federation support
Olympics minister Tessa Jowell and London Mayor Boris Johnson want Wembley Arena to host badminton and rhythmic gymnastics in the 2012 Games.
Ms Jowell originally wanted the events to take place in a temporary venue in north Greenwich, south-east London, at a cost of £20m.
The pair will now try to persuade the gymnastics and badminton world federations to choose Wembley Arena.
The International Olympic Committee has told London to "urgently" name venues.
The BBC understands that Ms Jowell will support the Wembley plan in return for Mr Johnson dropping his opposition to shooting events being based at the Royal Artillery Barracks in Woolwich.
The mayor's spokesman said: "The agreement is now a matter for the board and the mayor invites them to recognise this proposal, which has the full backing of the two people that are elected to represent the interests of London voters, taxpayers and the wider electorate."
The plan would save 2012 organisers £20m as they would no longer have to build and demolish the temporary Greenwich venue.
Adrian Warner, BBC London Olympics Correspondent
The venues row was one of the biggest controversies of the Games so far. 2012 have been trying to find agreement with the IOC and badminton and rhythmic gymnastics for more than a year now. But sports officials have been reluctant to make the move because it will mean more travelling for competitors from the Olympic village in Stratford in east London.
London 2012 chairman Sebastian Coe said he would also back the Wembley Arena plan if the two sport federations supported it.
But last month Badminton England said it was opposed to playing at Wembley Arena.
Its chief executive Adrian Christy said playing at Wembley would damage competitors performances due to the travelling time required from the athletes' village in Stratford, east London.
It came after the British Olympic Association opposed moving boxing events from the proposed ExCel Arena in east London to Wembley for similar reasons.
Last week Denis Oswald, chairman of the International Olympic Committee commission that monitor's London's progress, said the badminton and rhythmic gymnastics venues must be selected as a matter of urgency.
He said: "I have to express a concern that three years before the Games the venue has not been finalised."