Wates has already been working for the council to develop the construction programme and help get the designs through planning.
The centre is being built for the 2022 Commonwealth Games. It will have a 50-metre Olympic-sized competition swimming pool, a 25-metre diving pool and a studio pool along with seating for 1,000 spectators.
Construction work is expected to start in summer 2019 and the centre will be open to the public after the Commonwealth Games.
Alongside the swimming facilities the centre will also have a gym and activity studios, a sports hall, indoor cycling studio, sauna/steam room and a football pitch.
Wates Construction regional managing director John Carlin said: “It is a huge privilege to be appointed as the design and construction partner for this important community facility for Smethwick.”