Glanford Park came out top of a shortlist of four potential sites, which included Quibell Park and Central Park.
The complex will include an eight-lane swimming pool and six-court sports hall, it will cost approximately £12.4m to build.
Council leader Don Stewart said: "We are not frightened to make big decisions.
"Just think, as you come down the M181 and see the wonderful football club on the right and on the left we hope to see a wonderful sports centre."