The 18-year-old is understood to have impressed both Sir Alex Ferguson and reserve-team boss Ole Gunner Solskjaer during trials.
United have now handed Vermijl a three-year contract with his current club Standard Liege getting around €300,000 in compensation.
Wing-back Vermijl, who can play on either side, will move to Old Trafford in the summer.
"They said he was the best right or left-back they had seen in years," Vemijl's father Dirk told Het Laatste Nieuws.
"Ferguson told me that Marnick in the following years would become a fixture in the Manchester United squad."