The Belgian had been subject to plenty of transfer rumours throughout the window but has now completed a deadline-day move to Manchester United.
Lammens made 64 appearances for Royal Antwerp, keeping 12 clean sheets after joining the club from Club Brugge.
The shot-stopper is expected to replace both Altay Bayindir and Andre Onana as United's number one goalkeeper.
"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," Lammens told the club's website.
"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."
Jason Wilcox, Man Utd's director of football, added: "Senne is an excellent young goalkeeper with great potential; we are delighted that he has chosen to join Manchester United after significant interest from a number of clubs."