The Magpies announced the appointment of Bruce as head coach on Wednesday morning, with the 58-year-old penning a three-year deal.
Coaches Steve Agnew and Stephen Clemence will join him on Tyneside.
Bruce resigned as Owls manager earlier this week, with his manner of his departure having left a bitter taste in the mouths of Wednesdayites, with the club having now issued a statement following the announcement from Newcastle.
It reads: "The club is disappointed to learn via public statement issued by Newcastle United that it has appointed former Sheffield Wednesday staff Steve Bruce, Steve Agnew and Steve Clemence.
"Regardless of the fact that the staff resigned from their positions with the club on Monday, there remains outstanding legal issues to be resolved between the club and the staff and Newcastle United. The club is currently considering its position and taking the appropriate legal advice.
"No further comment will be made by the club concerning this matter."
Bruce's 18-match reign was the joint-shortest in Wednesday history alongside Peter Eustace, who managed the club briefly in the late Eighties.
On being unveiled as head coach at boyhood club Newcastle, Bruce said: "I am delighted and incredibly proud to be appointed as head coach of Newcastle United.
"This is my boyhood club and it was my dad’s club, so this is a very special moment for me and my family.
"There is a huge challenge ahead of us, but it is one that my staff and I are ready for.
"We will roll our sleeves up and we’ll be giving it everything from the off to ensure supporters have a successful team that they can be proud of.”
Lee Charnley, managing director at Newcastle, added: “Steve has a deep affection for Newcastle United and we are very pleased that a coach with his vast experience and connections to the club and city has joined us.
"Steve knows what this club means to supporters and to the region and he will put his heart and soul into leading our talented group of players with the full support of our staff.
"The hard work for Steve and his team starts immediately and we will be fully prepared for the challenge of a new Premier League season."