The goalkeeper has been a problem position for Man United for a number of seasons with Onana and Bayindir failing to establish themselves.
Ruben Amorim will doubtless be hoping Lammens, 23, will be a safer pair of hands after United confirmed his signing from Royal Antwerp on transfer deadline day.
According to The Athletic, Lammens joins the 20-time English champions for a fee of €21million (£18.2m) plus €4m in add ons.
Lammens travelled to Manchester on Monday to undergo a medical and put pen to paper on a five-year deal at the club.
Speaking to his new club, Lammens said: “I am extremely proud to be joining Manchester United; it is a real dream come true. The past few years have been an amazing journey; it’s now ended in an incredible destination and hopefully the beginning of something special.
“You can feel the positive atmosphere that is being created here, and I know that I can make a real impact at the club in the coming years.
“I cannot wait to get to know my team-mates and begin working with Ruben and the coaching staff. This is the perfect place to keep developing, grow together with this exciting team and achieve my career objectives.”