The 24-year-old joined Palermo in January 2014, initially on loan, helping them to the Serie B title in his first season before becoming a regular in the top flight.
The Morocco international has signed a five-year deal with the Magpies, keeping him at St James' Park until 2021.
"I am very happy to be at Newcastle United. I'm proud to sign here because Newcastle is a great team in England," he told the club's official website.
Manager Rafael Benitez added: "Achraf is a good, young player with international experience who has grown his game in Italy. He gives us width on the left, has a good left foot and will add great competition to the squad."
Lazaar, who becomes Newcastle's 11th signing of the summer, made 76 appearances for Palermo, scoring three goals.