The 21-year-old joins the Championship side on a three-and-a-half year deal for an undisclosed fee.
Goss had been a regular for United’s under-23 but never made an appearance for the first-team.
He said: “I’m delighted that the deal is done – absolutely buzzing.
“I’m at the point now in my career where I need to be playing First Team football, week in, week out – so the opportunity to move to QPR was just something I had to pursue.
“Ian (Holloway) and Les (Ferdinand) had a massive influence on me. They told me everything I wanted to hear.
Premier League Done Deals: Every transfer out during January 2017
Fri, January 27, 2017
Express Sport brings you up to date with every departure from the Premier League during the January transfer window
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“The way they both spoke about QPR, showing such passion for the football club, was really special.
“Now it’s up to me to repay them both and everyone else at QPR for showing their faith in me.”
Rangers boss Ian Holloway added: “I’m delighted we’ve managed to bring Sean to QPR.
“He’s a young player with great potential – and I feel there are players at Manchester United who can get a little bit lost, because they’ve always got the best of the best of the best.
“I’ve managed to borrow one or two from United over the years, but sometimes you spot one and you want him – and that’s exactly why I’ve bought Gossy here.
“I want to put my stamp and my name and the wonderful name of QPR on him – because I firmly believe he’s got a fantastic future ahead of him.”