Diaby has rejected the chance to play with Cristiano Ronaldo at Saudi side Al Nassr in favour of a move to Villa Park.
The 24-year-old has been a revelation since signing for Bayer Leverkusen from Paris Saint-Germain in 2019.
Diaby has netted 32 goals in 125 appearances for the Bundesliga club and has represented France ten times at senior level.
The winger is set to become Villa's third major signing of the summer following the acquisitions of Youri Tielemans and Pau Torres.
The Midlands club saw an opening offer of £30million plus add-ons rejected and were told to present an offer in excess of £50m.
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With a fee now agreed, Diaby is set to become the club's most expensive signing, eclipsing that of Emi Buendia who moved to Villa Park from Norwich for £38m in 2021.
Boss Unai Emery knows all about Diaby who impressed in Paris Saint-Germain's academy during the Spaniard's two-year stint in charge of the Ligue 1 champions.
The Frenchman will get another shot at European football next season when Villa kick off their Europa Conference League campaign.
Diaby was part of the Leverkusen team that reached last season's Europa League semi-final before suffering a narrow defeat to Jose Mourinho's Roma.
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