Pecchia had been Benitez's assistant since the Spaniard was in charge of Napoli, taking him to Real Madrid and later Newcastle.
However, after Newcastle were relegated to the Championship, Pecchia elected to move to Verona, who were also relegated to the second division this season.
Verona finished bottom of Serie A in 2015-16, winning just five of their 38 games.
Pecchia, 42, assumes the vacant role of head coach left by Luigi Delneri, signing at the Stadio Marc'Antonio Bentegodi on a one-year deal.
Newcastle released a statement on Wednesday, saying: "The club would like to thank Fabio for his services to Newcastle United during his time with the Magpies, and recognises that this is a fantastic opportunity for him to further his career.
"Good progress is being made with regard to replacing Pecchia, and a further announcement will be made in the coming days."