Esteem is made up of Morgan Sindall, Robertson Capital Projects and Sewell Group.
Vinci was also shortlisted for the scheme but dropped out of the race earlier this year.
Hull City Council said it would make an official announcement on the identity of the preferred bidder next week. Work is expected to start in March 2009.
Balfour Beatty confirmed on £20.9m roads jobNashville convention center should be decided on by public, Councilman Crafton says