Former Sunderland manager Bruce, 58, resigned as Sheffield Wednesday boss on Monday following talks with the Magpies at the weekend.
Newcastle have been without a manager since Rafael Benitez left when his contract expired in June, saying the club "did not share his vision".
Bruce was born near Newcastle and was a boyhood Magpies fan.
"There is a huge challenge ahead of us, but it's one that my staff and I are ready for," said Bruce. "This is my boyhood club and it was my dad's club, so this is a very special moment for me and my family."
Bruce will be joined by coaches Steve Agnew and Stephen Clemence, who have been part of his team at a number of his previous clubs.
Steve Bruce has been in managerial employment during every calendar year since his first job with Sheffield United in 1998.
Lee Charnley, managing director at Newcastle United, said: "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."
Newcastle are the 10th club Bruce has managed and this is his 11th post, having led Wigan Athletic twice.
Sheffield Wednesday issued a statement on Wednesday saying "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."
His appointment has prompted widespread debate among fans, with factions of the club's support still angered a deal could not be struck for Benitez to stay on at St James' Park after more than three years at the club.
Benitez was appointed manager of Chinese Super League club Dalian Yifang little more than a week after his departure and said his Newcastle vision was not shared with "those at the top of the club".
Owner Mike Ashley has drawn fierce criticism from Newcastle's support, with a perceived lack of spending often a focus of frustration.
Last week, former England boss Sam Allardyce said he had turned down the chance to be Newcastle manager.
Manchester City assistant Mikel Arteta had also been linked with the job, as were ex-Manchester United boss David Moyes and Belgium manager Roberto Martinez.
Bruce saw his Sheffield Wednesday side lose only three times in 18 matches after taking charge on 1 February, leading them to a 12th-place finish in the Championship.
He briefly delayed taking over at Hillsborough in order to recover from surgery and the death of both his parents in 2018.
Bruce will now fly to China to meet the squad following Wednesday's Premier League Asia Trophy match with Wolverhampton Wanderers.
Steve Bruce - competitive record (all comps)Games: 904 Wins: 348 Draws: 227 Losses: 329
Average win percentage: 38.5%
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