United landed Malacia in a reported £12.95 million deal after making a late move for the Netherlands full-back, who had been close to joining French club Lyon. The 22-year-old has agreed a four-year contract with the option of a further 12 months.
It is a landmark deal for Ten Hag, who had been linked with a host of potential signings before finally making Malacia the first acquisition of his United reign. Ten Hag arrived at United in May after finishing his successful spell at Ajax, where he had plenty of opportunities to see Malacia's quality with Dutch rivals Feyenoord.
Malacia, who made 136 appearances for Feyenoord, said: "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 leading us".