Lammens has already played 64 games for Royal Antwerp and helped them win the Belgian Super Cup in 2023.
The 23-year-old, who was named in the Belgium national team squad for the first time in March, kept the most clean sheets in the Belgian Pro League last season.
Senne 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.