Kozak agreed a four-year contract with the English Premier League club after coming to the attention of Villa manager Paul Lambert with a series of fine displays for the Italian side in last season's UEFA Europa League.
The 24-year-old was the top scorer in Europe's second tier competition with ten goals and Lambert admitted he had been tracking the player for some while.
"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," Lambert told Villa's website.
"Libor has an unbelievable scoring record in the Europa League, incredible really," Lambert continued. "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."
Kozak joined Lazio from Slezsky FC Oprava in 2008 and was soon loaned out to Brescia for whom he scored four goals in 22 appearances.
He eventually made 77 appearances for Lazio, scoring 22 goals, and has also won four caps for the Czechs, scoring once in a friendly against Hungary last month.
"I'm really happy to be at Aston Villa and I'm ready for this new step in my career," he said. "I hope it's a good step for me and also for Villa because everything is about the team.
"This is a big club, a very historic club with a fantastic fanbase and, for me, this is really important."