Work on the project, part-funded by a £2m Sport England lottery grant, is set to begin in February.
The centre will have a six-lane 25m swimming pool and a learner pool, a studio gym, sauna and steam rooms and an outdoor all-weather sports pitch.
The new facility on Scott Road will replace the former Abbey Leisure Centre that was destroyed by fire in February 2013.
Completion is scheduled for January 2015.
Designed by Bradshaw Gass & Hope, the leisure centre will have such energy efficiency measures as a combined heat & power (CHP) plant and LED lighting.
The project has been procured through the YORbuild construction framework.
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