The Telegraph reports that Villa will pay a club record £28m (€31m) for Watkins, 24, with the fee potentially topping £30m (€33.2m) after add-ons.
Watkins was named the Championship’s Player of the Year last season after he scored 26 goals for the Bees.
But Brentford’s defeat to Fulham in the play-off final meant a Premier League move was inevitable for Watkins.
A number of clubs have shown interest, but Villa have won the race with Watkins expected to undergo a medical in the next 24 hours.
Villa boss Dean Smith knows Watkins well, having coached him while in charge at Brentford.
Watkins’ arrival will follow that of defender Matty Cash, who Villa paid £14m to recruit from Nottingham Forest.
Smith’s side have also made a £16m bid for Bournemouth striker Joshua King.