The Swede moved to Old Trafford from Benfica in 2017 and has developed into a mainstay of the United defence since.
“Since the day I arrived at United it has felt like home," he told the club's official website.
"I have grown significantly both as a player and as a person in the last two years and for that I am grateful to everyone at the club for their help and support.
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"I love playing football and my aim now is to help the team to win trophies and repay the fans for their unrivalled support.
“I know that everyone at the club shares this vision and will give everything to get Manchester United back to where it belongs."
Manager Ole Gunnar Solskjaer added: Victor has established himself here and has become a very important part of our team.
"He brings calmness on the pitch and I can see that he is determined to help this club and to be successful here.
"I’m extremely happy that he has committed his future to Manchester United.
"We’re all looking forward to working together to deliver the success and get United back to where we know the club belongs."
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