Thiaw moved to England in a deal reportedly worth £30.3m (€35m/$40.8m), with up to £4.3m (€5m/$5.8m) in potential add-ons.
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The 24-year-old will wear the No.12 shirt for the Magpies, becoming their second permanent signing of the summer after Elanga, while Aaron Ramsdale has also arrived on loan.
"I'm really excited to join this massive club. I can't wait to start training and to get to know my new team-mates and all the staff,” Thiaw told club website.
"The gaffer showed me his vision and what he wants to do with me as a player and the club itself, which is really exciting.
"I think Newcastle speaks for itself. It's a great club, a big club with passionate fans who I can't wait to see at St. James' Park."