The 22-year-old Frenchman came through a medical on Wednesday and committed to the club until 2020.
Thauvin was identified as a potential signing by chief scout Graham Carr more than two years ago and the club has been monitoring his situation since.
The former England manager said: “Florian is a player the club have been watching for a long time and I am delighted that we have been able to sign him.
“He is a perfect signing for this club – someone who is young, with great potential and is one of the best young players in Europe.
“He is an exciting, creative talent who can score goals and make assists, and we believe he will have a very bright future at Newcastle.”
The France Under-21 international added: “I am delighted to be a Newcastle United player. I have come from France to a really big club and am very happy to be here.
“They have put their trust in me and I am looking forward to playing for the team.”
As part of the deal to bring Thauvin to St James’ Park, Remy Cabella heads the other way on a season-long loan, which will become a permanent move next summer.
Thauvin, who will follow in the footsteps of fellow French wingers David Ginola and Laurent Robert in pulling on Newcastle’s black and white stripes, is the fifth summer signing made by McClaren.
He joins Georginio Wijnaldum, Aleksandar Mitrovic, Chancel Mbemba and Ivan Toney through the door at St James’ Park and McClaren will hope his arrival kick-starts the Magpies’ Premier League campaign following a draw and a defeat from the opening two games of the season.
It does not get much easier for Newcastle as they head to Old Trafford to face Manchester United on Saturday, where Thauvin will be hoping to make his debut.