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The Owls have now paid out £125,000 to sign the Scot, beating off competition from three other clubs including Hull City.
Bristol City had also agreed a fee with Rangers, but he is believed to have prefered to stay in the north.
He will join Lee Peacock who also recently moved to Hillsborough despite interest from Hull.
Wednesday boss Chris Turner described MacLean as "one of the hottest prospects to come out of Scotland" after signing him on a three-year deal.