The £125m Scottish National Arena will feature capacity for 12,000 when it opens in 2013, ahead of the Commonwealth Games the following year.
Scottish Exhibition and Conference Centre (SECC) is the lead partner on the project, which has been designed by architecture firm Foster + Partners.
Glasgow City Council and Scottish Enterprise are also partners on the scheme.
SECC chief executive John Sharkey said: "It is our commitment to work with the very best in the business to achieve our vision for the Scottish National Arena as one of world’s leading venues. Bovis Lend Lease has a proven track record of delivering our requirements on schedule and with their experience and capabilities, they will help us make our vision a reality."