The Owls sacked Gary Megson on Wednesday, despite the club being in third place in League One.
Jones has signed a thee-and-a-half year contract with Sheffield Wednesday.
“Promotion is the first ambition and from there is to try and get to the Holy Grail, which is the Premiership,” Jones said.
“I’ve had a lot of calls asking why I have dropped down to League One but I don’t see it that way. I look at the size of the club and think this is a club that can go places.
“After talking to the chairman and seeing what he wanted and what his plans are, I had no hesitation in choosing here because it is a huge club that should not be where it is now.”
Sheffield Wednesday chairman Milan Mandaric said: “Dave is a very successful football manager and I am delighted to welcome him to Sheffield Wednesday.
“It was essential we made a swift appointment with 13 games to go this season and I am convinced we have the right man for this job.
“I like his style of football and his approach to the game but more than anything else, he is a builder of clubs and he will help to galvanise Sheffield Wednesday.
“His first objective is to get us out of League One and back into the Championship and then rebuild the club for the Premier League.
“I always look for someone who shares my ambitions and my objectives and Dave Jones is that man.”
