The Midlands side moved quickly to seal a club-record £33million deal ahead of Arsenal, who missed out on the Argentine.
The 24-year-old was named Championship Player of the Season as the Canaries stormed to the title and return to the Premier League at the first time of asking, but will be playing his football at Villa Park next season.
Buendia will complete his medical and transfer after leaving Argentina’s biosecure bubble later this week.
In a statement, Villa said: “Aston Villa and Norwich City have reached an agreement for the transfer of Emiliano Buendia.
“As Emiliano is currently in the Argentina national team’s biosecure bubble, preparing for a World Cup qualifying match with Colombia on Tuesday evening, he will undergo a medical and complete the transfer after the game.”
Villa are also thought to be interested in Southampton captain James Ward-Prowse, though the Saints are set to reject any approach for the England midfielder, who has four years remaining on his deal.