Despite being overlooked for the pre-season tour of Australia and Asia, the 19-year-old has gone onto enjoy an impressive breakthrough campaign at Old Trafford.
Academy graduate Williams has made 33 first-team appearances for United, having made his debut off the bench in September's Carabao Cup clash against Rochdale.
The full-back signed an improved contract until at least 2022 the following month, but his continued progress has seen him rewarded with a deal until 2024 with the option of a further year.
"Signing this contract is another really proud moment for myself and my family," Williams said.
"Having been at Manchester United since I was seven years old, it's genuinely a dream come true to be playing in the first team.
"It has taken a huge amount of hard work to reach this point and it has been really special for me to break through into the squad.
"I've learned a lot throughout the season from the manager, his coaching staff and my team-mates and I want to repay the trust that they have all shown in me.
"I know that everyone at the club is working really hard every day to achieve success in the coming years and I am really excited to be a part of that."
Williams has a big few weeks coming up with fellow left-back Luke Shaw absent for United's Europa League campaign through injury.
Manager Ole Gunnar Solskjaer said: "Brandon has had an excellent first season, so we are delighted that he has signed a new contract.
"This new deal is a real testament to his hard work and the progress that he has made since his debut.
"Brandon never looked back after stepping up from the academy and having come all the way through the system he understands what it means to play for Manchester United.
"He has all of the attributes required to be a member of this exciting young squad.
"He will continue to learn every day in training and we look forward to watching him develop over the coming seasons."