The French striker, who almost moved to St James's Park in January before opting instead for a switch to Loftus Road, netted six goals in 14 appearances for Rangers over the last four months of the season.
The 26-year-old was unable to prevent Harry Redknapp's side from being relegated to the Championship but will now spend the 2013/14 campaign back in the Premier League.
Remy said in a statement: "I'm very happy to be a Newcastle player. It will be a huge honour to play for such a big club.
"I was very flattered by the club's interest in me back in January and also very happy that they showed interest in me again this summer.
"The Premier League is the best league in the world and that's where I want to play.
"I am very motivated this year to get into the World Cup squad for my country and I know in order to do that I need to have a big season and a successful campaign with Newcastle United."
Newcastle's director of football Joe Kinnear added: "The need for us to strengthen up front was a priority and I have been working very hard to secure one of our targets in this position.
"Now we have him I'm sure he'll be a huge success for us. I know he's hungry for goals and is absolutely committed to helping us achieve success this season."