The new complex will include two swimming pools, a gym, sauna and steam room.
The new development is at the site of the former Abbey Leisure Centre, which suffered a devastating fire in February 2012.
The council is hoping that Sport England will make a significant contribution towards the costs of the new centre.
Six contractors have now been shortlisted for the job – BAM, Esh, ISG, Kier, Wates and Willmott Dixon.
Work is expected to start on site in November and be complete by Christmas 2014.
Deputy Leader of the Council, Cllr Gillian Ivey, said, “This has been an important step for our new leisure centre, which will deliver first class facilities for the district.
“The fire at the old Abbey Leisure site was obviously a huge blow, but it’s also been an opportunity for us to create something brand new and really exciting at the site.
“With its range of facilities this new development will be a real draw for the area, supporting not only those using the new centre but also with a knock on benefit to local businesses too.”