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The 29-year-old had spent the second-half of last season on loan at Old Trafford where he put in some solid performances.
He scored three and assisted one across 18 appearances before his season was cut short by a knee injury, helping the Red Devils win the Carabao Cup and reach the FA Cup final.
At the end of May it was reported that United were not interested in making the loan permanent however, despite being available for just £18million, with Erik ten Hag wanting to bring in a younger midfielder.
The manager got his wish with Mason Mount arriving from Chelsea, but just a few weeks ago it was said that United had not actually entirely ruled out signing Sabitzer as they look to further strengthen their squad depth.
But that chance has gone for good now, with Dortmund confirming the signing of the Austria international from bitter rivals Bayern on Monday evening.
Sabitzer has moved for a fee of around £16m and has penned a four-year deal with his new club.
‘I can hardly wait to finally join the team and wear the BVB jersey,’ he told Dortmund’s official website.
‘The talks with the Borussia Dortmund management were outstanding and have shown me how ambitious the club wants to be in the coming years.
‘I would like to play my part in ensuring that BVB achieve their objectives and have every reason to celebrate something special with their fans again as soon as possible.’
After a brilliant spell with RB Leipzig, Sabitzer joined Bayern just two years ago, though struggled to make an impact, making just four goal contributions in 54 games.
Nevertheless, he leaves the Allianz Arena a Bundesliga winner and will be expected to directly replace England midfielder Jude Bellingham who left for Real Madrid earlier in the window for an initial £88.5m.
MORE : Tottenham outcast Davinson Sanchez in advanced talks to join Spartak Moscow
MORE : Manchester United dealt transfer blow as Leon Goretzka reaffirms commitment to Bayern Munich
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