Gray has overseen just two defeats since taking temporary charge at Hillsborough in the wake of Dave Jones' December departure.
That run has taken Wednesday clear of the Championship's bottom three, and Saturday's win at Rochdale booked a place in the last 16 of the FA Cup.
Milan Mandaric has rewarded Gray with the role on a full-time basis, and the owner said: "I am very happy.
"When he was initially asked to step in, his brief was to get us out of the bottom three, get some wins and clean sheets, and make some tangible progress on the pitch.
"Stuart has achieved all those things, he was given the chance to impress and has taken that chance with both hands."
Gray's official title is head coach, and Mandaric's longer-term aim is to appoint a director of football as part of a new management structure.
He said: "I am looking at the bigger picture for where this club needs to go and in a modern football environment for the long term benefit of Sheffield Wednesday.
"This is a big club that needs to go places and this will modernise the structure of the football side."