The Czech Republic international attracted Villa manager Paul Lambert's attention with an impressive return of 11 goals in 18 UEFA Europa League games.
Despite failing to find the target in Serie A last term, Lambert is confident that Kozak will help to ease the side's reliance on Christian Benteke, who netted 19 Premier League goals last term as Villa flirted with relegation.
"We've been on this one for the last few months, trying to bring him to the club, so I'm delighted to get it across the line," the Scot told the club's official website.
"Libor has an unbelievable scoring record in the Europa League, incredible really.
"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.
"Libor's powerful, too, and I'm looking forward to working with him. We needed to bring in someone like Libor to help the overall philosophy to work.
"It's a matter of him now integrating with the group, which he'll do. We've brought in seven players this summer and we're trying to build the squad. It's getting there, no doubt about that and we'll keep building it."
