The 22-year-old will join the club on a reported three-year contract having seen out his deal with Reims.
He told reporters: "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."
The Magpies, who finished fifth in the Premier League last season, will play Europa League football in the new campaign.
Amalfitano takes Newcastle's number of France-born players to seven.