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Toure, the former Arsenal, Manchester City and Liverpool defender, was appointed Wigan manager on November 29. It was his first job in management.
However, the 41-year-old was sacked on Friday (AEDT) after just 59 days having failed to win any of his nine games in charge.
Toure's Wigan lost six of those fixtures and sit bottom of the Championship with 25 points from 28 matches.
The Latics' chief executive Malachy Brannigan said: "Firstly, I'd like to thank Kolo [for his] efforts during [his] time at the football club.
"Unfortunately, the results on the field have not been as we would have liked and as tough a decision as this was, the Board felt it necessary to give us the best possible chance of remaining a Championship club next season."
