Pereira is now committed to the Old Trafford outfit until 2023, with the option to extend for a further year.
The 23-year-old, who came through the United academy, enjoyed a breakthrough 2018-19 campaign and has made 35 first-team appearances.
After beginning the campaign on the fringes of selection under Jose Mourinho, he was given a run in the side in the second half of the season by Ole Gunnar Solskjaer.
Transfer verdict 2019: Stay or go?
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Pereira told the club's website: "I have spent so long in Manchester that I now regard the city and the club as my home and I'm extremely happy to continue my career here.
"The manager has shown great faith in me and I can't wait to get this campaign started under him."
Pereira joined the United Academy during the 2011-12 season and has previously had loan spells at Granada and Valencia.
United boss Solskjaer believes he has the mentality to succeed at the club.
Solskjaer said: "Andreas is another player brought through our Academy that understands what it means to play for Manchester United.
"He came from another country but quickly understood the values of playing for this club and doesn't take it for granted.
"Andreas has become an important member of the squad with his energy and hard work in midfield.
"He works non-stop every day in training, has a great character and knows what he has to do to continue his development here."
Meanwhile, Tuanzebe has committed his future to the club by signing a deal that keeps him at Old Trafford until 2022 with the option of a fourth year.
Tuanzebe, 21, is a product of the club's youth academy and spent last season on-loan at Aston Villa, where he helped the club win promotion to the Premier League via the play-offs.
The defender, who will join the first team on their pre-season tour, said: “I have grown up at Manchester United and it has always been a big part of my life and my family’s life. I appreciate the trust that the club has in me and I want to repay that with my performances on the pitch.
“I know I have a lot of hard work and learning ahead of me but the experience I gained throughout last season puts me in good stead for the future ahead. I am determined to give everything and show everyone the player that I can be.
“I can’t wait for the tour to get started and to see what the upcoming season brings.”
Manager Solskjaer said the youngster is a player that other members of the academy should look be inspired by.
“Axel is a great example of the type of player that has come through the Manchester United system. He is humble, hard-working, talented and a team player," he said.
“He had a successful time on loan with Aston Villa and has gained a lot of experience from that spell, which ended in promotion to the Premier League. He will come on the pre-season tour with us which will help his development further.”
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