Final costings for the project have now been confirmed at £73m up from an initial estimate of £60m.
The rise in the final budget reflects updated costs for groundworks, construction prices and contingencies built-in by the council and the Birmingham 2022 Commonwealth Games budget.
Councillors are set to sign off funding and contract agreements at a meeting next week.
Work to prepare the site is already well advanced with the main building work set to start in January.
The world-class facility at Londonderry Lane in Smethwick will host the swimming and diving events at the Birmingham 2022 Commonwealth Games.
Sandwell Council will contribute £27m with £38.5m coming from the Birmingham 2022 Commonwealth Games budget.
A further £7.6m is funded by other external partners Sport England, Black Country LEP, Sandwell Leisure Trust (SLT) and University of Wolverhampton.
Sandwell Council had already budgeted to build a new leisure centre for Smethwick and can now provide a much bigger, improved facility at a similar cost to the authority – thanks to additional funding brought in by hosting the Commonwealth Games.
When complete, the centre will have a 50m Olympic-sized swimming pool, a 25m diving pool and a studio pool along with 1,000 permanent spectator seats. Additional seating will be added on a temporary basis for the Games.