According to RMC Sport, the 18-year-old is expected to travel to Birmingham on Saturday for his medical and to complete the final formalities of his move.
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Mbaye is set to sign a five-year contract with Unai Emery’s UEFA Europa League winners.
Villa have been long-term admirers of Mbaye and gradually stepped up their pursuit before reaching an agreement with PSG on Friday.
RB Leipzig, Chelsea and Liverpool had also shown interest in the teenager. Liverpool eventually withdrew from the race after PSG’s initial demands approached €70m.
Villa’s eventual €55m package represents a significant investment in the highly rated youngster, who will now prepare for the next chapter of his career in the Premier League.