The 22-year-old has become Erik ten Hag's first arrival at Old Trafford in the current transfer window and has agreed terms on a deal until the summer of 2026.
Man United are believed to have forked out an initial fee of €15m (£12.9m) to sign Malacia, which could rise to as much as €17m (£14.6m) with performance-related bonuses.
Malacia departs Feyenoord after spending 14 years with the Rotterdam giants since joining their youth setup in 2008, scoring four goals and setting up 10 more in 136 games for the club.
"It's an incredible feeling to have joined Manchester United. This is a new chapter for me, a new league with new team-mates and a tremendous manager [Erik ten Hag] leading us," Malacia told manutd.com.
"I know from playing against his teams in the Eredivisie, the qualities that he has and what he demands of his players.
"Whilst I know that I am still young and will continue to develop, I can promise the United fans that I will leave everything on the pitch every time I pull on the red shirt. I'll always be thankful to Feyenoord for all they have given to me and my family.
"None of this would be possible if it wasn't for them. Now I'm ready to focus on the future with United, and help my new club achieve success."
Director of football John Murtough added: "Tyrell is an exciting, dynamic young footballer with excellent experience for his age, including five seasons in the Eredivisie, a European final and full international honours for the Netherlands.
"We look forward to seeing him continue to develop under the guidance of Erik ten Hag and his coaching team in the years ahead. Everyone at Manchester United welcomes Tyrell to the club."
Malacia's 2021-22 season saw the left-back score one goal and set up five more in 50 outings in all tournaments, helping Arne Slot's side reach the final of the Europa Conference League before their defeat to Roma.
The defender won one KNVB Beker and one Dutch Super Cup with Feyenoord, and he has already earned five caps for the Netherlands national team, providing two assists.
Malacia had recently confirmed to De Telegraaf that his move to Man United was imminent while paying tribute to Feyenoord, saying: "Mr Ten Hag is a very good coach and also a warm person, so I had a good conversation with him and I have a very good connection with him.
"That's important, because if all goes well we'll be working together for many years. I'm looking forward to that, because I think I can learn a lot from him. He has a record for improving players individually, as long as they are prepared to work hard.
"My team-mates at Feyenoord were very sad because I played together with some for so long and we really built a bond. Everyone wished me the best and I will always keep in touch with a lot of those guys.
"Feyenoord is my club - and it always will be. I am a boy of the club and of the city, so yes Feyenoord is my home and is forever in my heart."
Malacia is now due to link up with the Man United squad ahead of their pre-season tour of Thailand and Australia, which begins with a clash against Liverpool on July 12 in Bangkok. body check tags ::