Detailed plans for the design of the building, which is expected to create up to 500 jobs and open in 2012, are now being considered.
Work is due to start on the venue later this year and to be completed in 2012.
Building of the 13,500 seat venue will safeguard around a hundred existing jobs in construction provide 90 new apprenticeships.
The 13,500 capacity stadium will add £25m a year to the Leeds economy.
BAM is leading on a £9.2m refurbishment of the Leeds City Varieties theatre and previously constructed the Leeds Metropolitan University building, the Rose Bowl.