The 21-year-old made his debut at Old Trafford during last season's League Cup win over Newcastle United, but that remains his only appearance for the Red Devils.
Vermijl, a Belgium Under 21 international, will join fellow new signings Samuel Stefanik and Jakob Jantscher at the Eredivisie club, as confirmed by former player Edo Ophof.
"Vermijl is a right-back who has defensive and attacking qualities. Also, he gained a fantastic football education at Manchester United," Ophof told NEC's official website.
"The first-team squad of NEC was in need of direct reinforcements. With the signing of these three players the squad gets a direct quality boost.
"Midfielder Stefanik and all round attacker Jantscher are strong players who could just give that little bit extra that a team needs."