The left back was a key priority for Rafa Benitez, with the club finally getting him a suitable player in that position.
Barreca has played eight games for Monaco since July. He will be hoping that he can get a regular starting spot on Tyneside.
The Barreca deal follows soon after Newcastle secured the signing of Miguel Almiron from Atlanta United for a club-record fee.
Barreca told NUFC TV after the move was completed: "I am very happy to be here. I have accepted this challenge with a great deal of enthusiasm and I can't wait to start.
"I know that Newcastle is a big and historic club. I know that the people here really love football and that the fans are really behind the team. I think that the Premier League is the best league, so for me this is further motivation to do well."