Bruce's long-time coaching associates Steve Agnew and Stephen Clemence will look after the first team for the intervening period.
Bruce, 58, has achieved four promotions from the Championship but was most recently sacked by Aston Villa in October after failing to get a talented squad out of the second tier.
Wednesday will be Bruce's 10th managerial post of a journeyman career that has also seen him take charge of Sheffield United, Huddersfield Town, Wigan Athletic (twice), Crystal Palace, Birmingham City, Sunderland, Hull City and Villa.
He succeeds Jos Luhukay, who was dismissed on December 21 with the club languishing towards the bottom of the Championship.
Caretaker boss Lee Bullen has since overseen a revival with a four-match unbeaten run that has taken them up to 16th. Bullen will remain at Wednesday in a senior coaching role.