The Hungarian striker, who arrived in Gelsenkirchen from 1. FSV Mainz 05 last summer, is now preparing to represent his third club in the Bundesliga, having also previously played in VfB Stuttgart's youth and reserve teams.
"If I was ever going to move, then Hoffenheim were always going to be my first choice," said the 26-year-old, who also counts Real Madrid CF on his list of former clubs. "I like the mentality and the character of this team."
"It was not an easy situation for Adam," said Schalke's sporting director Horst Heldt. "He would have liked to play more than he did last season. Even though he didn’t always get much of a chance, he still scored plenty of important goals for Schalke and we wish him all the best for his future."
Szalai scored seven goals in 28 league appearances for the Royal Blues and featured nine times in their UEFA Champions League campaign, netting twice in last season's play-off against PAOK FC that took the club to the group stages. In total he has bagged 28 goals in 107 top-flight matches in Germany.