The 22-year-old Dutchman, who looked to be on his way to Olympique Lyon last week, has signed a four-year contract with the option for a further year.
Malacia is a full Dutch international, winning five caps to date.
He came through the Feyenoord youth ranks, going on to make 136 appearances for the senior team, including 50 times last season when they reached the Europa Conference League final, losing to AS Roma.
"It's an incredible feeling to have joined Manchester United," Malacia said. "This is a new chapter for me, a new league with new team-mates and a tremendous manager leading us.
"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."
Malacia will compete with Luke Shaw and Alex Telles for a starting berth at left back.
