Pecchia has assisted Rafael Benitez at Napoli, Real Madrid and St James' Park, but has opted to move into management himself having been offered the role at the Italian outfit.
Verona, like Newcastle, were relegated from the top flight in the season just finished, and Pecchia will be charged with taking them back into Serie A next term.
"Newcastle United have this evening confirmed that first-team coach Fabio Pecchia will be leaving the club to become manager at Italian club Verona," read a statement from the Magpies.
"Good progress is being made with regard to replacing Pecchia, and a further announcement will be made in the coming days."
Benitez added on his own website: "I am sad to see him depart as he has been an excellent professional from the first day and until the last in the years we have worked together.
"Second and most importantly, I am pleased because he has been considered for this new position, he leaves to face these new and exciting challenges, both personally and professionally."
Benitez has signed a three-year deal with Newcastle despite their relegation to the Championship.