The 24-year-old, who was top scorer in the Europa League last season with 10 goals, has signed a four-year contract at Villa Park.
"Libor has an unbelievable scoring record in the Europa League, incredible really," said Villa manager Paul Lambert of the 6'4" Czech international on the club's official website.
"He wasn't given much opportunity for Lazio in Serie A but he showed proper potential in leading the line there at a strong club with a great tradition and we need somebody like him as we only have Christian Benteke really as a main target man.
"He'll take that burden off Christian and he'll add greatly to what we've got, with the likes of Nicklas Helenius, who's a different type of player, Gabby Agonlahor, Aleks Tonev and Andi Weimann in that area of the pitch where we can hurt teams."
Kozak, who has made four international appearances for the Czech Republic, will wear the number 27 shirt at Villa.