The 22-year-old left-back became United's first signing of the summer this week in a deal worth £13m and £1.7m in add-ons.
Malacia amassed over 130 appearances for Feyernood and currently has 5 caps with the Netherlands.
Speaking following the official announcement, United's football director Murtough said: "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."