When the contract notice was published last year, the council envisaged a £15m price tag but councilliors have agreed to swallow the cost increases.
The new Bloxwich leisure centre will be built on part of Leamore Park to the rear of the existing site. The existing centre, opened in 1991, will then be demolished.
The new Oak Park centre will be built on playing fields to the rear of the existing site. Here, too, the current facility will then be pulled down and the playing field area reinstated.
Both new developments will have a 25m eight and six lane swimming pools, sports halls, 100 station fitness suites, dance studios, squash courts, café and upgraded external pitches swimming pool, squash courts, dance studios and fitness facilities.
The new buildings are scheduled to open to the public in December 2015.