Williams had been given the number 21 shirt at the Canaries.
Having graduated through the youth ranks of Manchester United, Williams made his Premier League debut against Liverpool in October 2019 before gaining a first league start for United against Brighton and Hove Albion on November 10, 2019.
Williams after completing his loan move said;
"It’s a massive club and I like the way they play. I’ve watched them over the years and seen how they play.
"The club like to play out from the back and play football. That really inspired me to come here, and I think that the head coach can really improve me as a player.
"Everyone has been so welcoming. I’ve really enjoyed my time here already and I can’t wait to meet everybody. I’ve just got a feeling it’ll be a good year."
Head coach Daniel Farke said: “We’re really happy that we have been able to bring Brandon in. This is an exciting deal for all parties, and we thank Manchester United for allowing us the opportunity to work with Brandon.
"Brandon is a young player full of potential. He has already proven that he can perform on the top level and that he is capable of playing for Manchester United. He has many good skills and qualities.
"We wanted to bring someone in who was capable of playing in the full-back positions to strengthen our squad. Brandon has played a lot at left-back for Manchester United, but we know he is also capable of playing on the right side, too.
"With Dimitris Giannoulis we have had only one natural left-back. For that, it’s good to have Brandon in the building and hopefully he can help us achieve our targets.”
