The forward trained with the Championship club on Tuesday morning but terms have since been agreed and he was expected to travel to the Midlands for a medical.
Villa boss Dean Smith was in charge of the Bees when they signed Watkins from Exeter in 2017 and made him his top target in attack when Brentford were beaten by Fulham in the play-off final.
Aston Villa are set to make Ollie Watkins their record signing after agreeing £33million deal
TOP FIVE MOST EXPENSIVE CHAMPIONSHIP SIGNINGS
Nathan Ake: £40m
(Bournemouth to Man City)
Moussa Sissoko: £30m
(Newcastle to Tottenham)
Jordan Pickford: £25m
(Sunderland to Everton)
Georgino Wijnaldum: £24m
(Newcastle to Liverpool)
Ryan Sessegnon: £24m
(Fulham to Tottenham)
Smith has been desperate to sign a striker ever since Brazilian forward Wesley sustained a serious knee injury at Burnley on New Year's Day.
Mbwana Samatta was signed from Genk for £8.5m that January, but the Tanzanian forward managed only two goals in the second half of the campaign.
Last season Watkins established himself as one of the most impressive forwards outside the Premier League with 26 goals to help Brentford finish third in the second tier – even though they were unable to complete the job in the play-offs.
His departure would represent a huge profit for the west London club, who bought him for about £2million.
While the £33m fee would be a club record for Villa, it would also make Watkins the most expensive player to come from the Championship.
While Nathan Ake cost Man City £40m from newly-relegated Bournemouth, and Moussa Sissoko set Tottenham back £30m in 2016, neither man had played in the Championship before making their big-money moves back to the Premier League.
Watkins can also operate in wide areas, which would be a huge bonus to Smith who has been looking to revitalise his front line.
The Brentford man scored 26 goals in all competitions as a striker last season
Watkins had attracted a lot of interest from several Premier League clubs, with Tottenham, Crystal Palace and West Ham all keeping tabs on the forward.
However, it is Villa that has won the race for the highly-rated Bees star.
After missing out on Callum Wilson, who joined Newcastle, Villa have turned their attentions to his former Bournemouth team-mate Joshua King, and they are also keeping a close eye on Liverpool youngster Rhian Brewster.
Like Watkins, Brewster has never played in the Premier League but the 20-year-old made a huge impression on loan at Swansea last term, scoring 11 goals in 22 appearances in all competitions during the second half of the campaign.