Saliba put pen to paper on a five-year deal running to June 2031.
The fee represents a substantial increase on the roughly €2m Anderlecht paid CF Montréal for him just over a year ago, reflecting his rapid progression in Belgium, where he made 50 appearances and scored five goals for the Brussels club.
"I'm very happy to arrive at a great club like this. I'm excited about the project and I want to bring my qualities here and improve as a player. We have a great team, with great players and a fantastic coaching staff.
"It means a lot. Since I started my career, I've fought for an opportunity like this, to join a great club like this. Playing in the Champions League is a great dream for every player.
"It's really exciting. I'm very keen. It's a big step in my career to play for Villarreal," Saliba said.
Asked to describe his own game, the Canadian pointed to work-rate and directness as his defining traits.
"I'm going to bring a lot of work. I like to attack and defend for the team, to be aggressive and direct with and without the ball. That's my main quality. I want to help the team with goals and assists, especially in attack," he said.
Chief executive Fernando Roig Negueroles praised the effort Saliba made to push the move through and suggested Villarreal's transfer business for the summer was now effectively complete.
"We're grateful to Nathan for the effort he's made to come here, which was significant. He's excited to be here, I hope it's very satisfying for both parties and we hope he's here for many years. We follow a lot of players every year from every league.
"There were reports on him from MLS, but in Europe he's done well. He's fitted in terms of quality and characteristics. He's a player who has shown he can play for our team perfectly. And his youth helps us think he's a good player for now and for the future," Roig said, before addressing the squad's readiness for deadline day.
"Until the day it closes you never know, but we're very happy with the squad we have. What happens elsewhere doesn't depend on us — at most we can stick to the release clauses. We'd like not to lose anyone and to keep the squad we have right now."