In his five years at the Stadio Olimpico, which included a season on loan at Brescia, the Czech international scored 22 goals, while also finishing top of the charts in the Europa League last season with seven.
Tare, impressed with Kozak's commitment, revealed that the Biancocelesti compromised on price when he asked to leave in search of regular first-team football.
"Kozak to Aston Villa? He had asked to go away and we satisfied him by lowering our financial demands," Tare told Lazio Style Radio.
"I thank him for what he gave to Lazio, he is one of the most professional players I've ever known."
The Villa striker has scored one goal in four games for his country.