The 22-year-old arrives at Anfield after British media reported Liverpool paid a 70 million euros ($76.37 million) release clause in his contract.
Szoboszlai becomes the club's second recruit under new sporting director Jorg Schmadtke after Argentine Alexis Mac Allister as Liverpool look to revamp their midfield following a disappointing season.
The Hungary international scored 20 goals and provided 22 assists in 91 games since joining Leipzig in the 2021 winter transfer window.
Szoboszlai helped Leipzig win back-to-back German cups, and scored their second goal as the beat Eintracht Frankfurt 2-0 in last season's final in early June.