The club's director of football Horst Heldt praised the deal, which he believes brings much-needed competition to the Schalke strikeforce.
"Adam Szalai is an outstanding striker who had a good goalscoring record in Mainz," Bundesliga.com quotes Heldt as saying.
"Last season showed that our squad needs adding to. Professional competition is important for us in trying to achieve our objectives. Adam is at a very good age and has a strong character. He is a hungry player and wants to achieve great things at Schalke."
The Hungarian international has scored seven goals in 16 appearances for his country.