Former Leeds United and Swansea City boss Monk has been out of work since being sacked by Birmingham in June after guiding the club to 17th in the Championship last season.
Coach Lee Bullen was the interim caretaker boss of Sheffield Wednesday for the club's first six league games of the season, winning three to leave them 11th in the league table.
Monk's first game in charge will be after the international break at Huddersfield Town on 15 September.
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