Chris Turner had been chasing the left-back for quite a while and was very keen on signing the left-back from Livingston, where his contract expired on Monday.
McAllister was pondering a move south of the border and it was only recently that he made his debut for the Scots against Trinidad and Tobago.
Hearts have chasing a left-sided defender for a while now and Jambos boss Craig Levein was delighted to acquire his services after tough competition from Wednesday for his signature.
McAllister would have had to battle it out with Paul Heckingbottom for the first-choice left-back role if he had signed with The Owls.
So far, the Wednesday manager has made eight signings: Heckingbottom, David Lucas, Jon-Paul McGovern, Patrick Collins, Lee Bullen, Glenn Whelan, Guy Branston and Chris Marsden, who will complete his deal today.
Two new strikers and the possibility of another defender and midfielder should complete Wednesday’s pre-season business.