"I am really proud to be able to play for this club, and I am really excited at the challenge that lies ahead.
"St James’ Park is a really impressive and special stadium. In France, there is nothing that compares to this, and I can’t wait to get out there with my new team-mates and help the team climb the table."
Newcastle head coach Steve McClaren said: "Henri is someone the club have been watching for a while, and he has developed into an excellent player at Bordeaux.
"This is someone with a very good mentality, who is a tough player and a winner. Those are key qualities you need in the Premier League and we are looking forward to seeing him pulling on the Newcastle United shirt."