The Feyenoord boss, who will start his new role on June 1, replaces Jurgen Klopp, who took charge of his final Liverpool game against Wolves on Sunday after the German spent the last nine years at Anfield.
Sky Sports News understands Slot has signed a three-year deal that runs until the summer of 2027.
Slot secured the Dutch Cup in April and led Feyenoord to their first title in six years in the 2022-23 season.
Slot had previously been approached by Tottenham, Chelsea and Leeds. He signed a new contract last May to keep him at Feyenoord until 2026 but had referenced a desire to make the next step in his career.
