The Spaniard joins the Europa League holders on a three-year deal with his release clause set at €20million (£14.58m).
The 30-year-old joined Juve from Atletic Bilbao in 2013 and scored 27 goals in 92 games for the Serie A champions.
Llorente, though, has been deemed surplus to requirements in Turin follwing the arrivals of Paulo Dybala and Mario Mandzukic.
Sevilla have been on the hunt for a striker since selling Carlos Bacca to AC Milan earlier this summer. They will present their new number 24 to the media on Friday evening.