"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.
"From when I was a young boy, I have dreamt of playing in the Premier League and to do this with a club such as Villa is incredibly motivating. It's real now and I'm very happy about this."
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.
The forward played for Lazio 77 times in total, scoring 22 goals.
