The 22-year-old, who is out of contract at the promoted French club, will officially become a Magpies player on July 1.
His arrival was confirmed by the Magpies on Wednesday afternoon, although no details of the length of his contract have been released.
Amalfitano, whose older brother Morgan plays for Marseille and France, said: "I am very happy to be a Newcastle player. I have seen a bit of the city already and it is a change from France, but one I am really looking forward to.
"When a club like Newcastle wants you to play for them, it can only be a good thing.
"I have taken the opportunity to play in the Premier League and cannot wait to get going."
An attacking midfielder, Amalfitano previously played for Evian in the second division.