The 25-year-old is believed to have cost around £5million from French side Bordeaux.
Saivet said: "I am very happy to be here at Newcastle. 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."
Coach Steve McLaren added of the Magpies' first signing of the January transfer window: "Henri is someone the club has 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."
Saivet scored 23 goals in 178 appearances for Bordeaux after making his debut for the club as a 17-year-old.