The 22-year-old, part of the Netherlands squad at Euro 2024, has agreed a six-year deal to become the club’s second most expensive signing behind Moussa Diaby.
Maatsen underwent a medical in Germany earlier this week after agreeing personal terms with Villa.
The PSV Eindhoven academy product spent last season on loan at Borussia Dortmund and started last month’s Champions League final.
Dortmund were keen to make the deal permanent but could not match Chelsea’s valuation, with Villa eventually agreeing a deal worth a little more than his £35m release clause.
Teenage forward Omari Kellyman will join Chelsea for £19m in a separate deal, while Maatsen’s arrival will likely see one of Alex Moreno and Lucas Digne depart Villa Park.
Midfielder Douglas Luiz is, meanwhile, poised to complete his £42million move to Juventus this weekend.
Luiz, currently with Brazil at the Copa America, has undergone a medical in the US ahead of the switch which will end a five-year stay at Villa Park.
Signed from Manchester City for £15m following Villa’s promotion back to the Premier League in 2019, Luiz has made more than 200 appearances in all competitions.
His sale will be essential in ensuring the club comply with the league’s profit and sustainability rules, with the fee received banked as profit in the 2023-24 accounting year which ends on Sunday.
In a separate deal, Villa are signing midfielder Enzo Barrenechea and winger Samuel Iling-Junior from Juventus from a combined £21m.
