The 23-year-old defender came through a medical on Tyneside on Tuesday after the clubs agreed a fee last week, and Newcastle confirmed that he had signed a five-and-a-half-year contract with the club.
"It is an honour to be able to come to Newcastle United and have the chance to play in the Premier League," Yanga-Mbiwa told the Newcastle website.
Yanga-Mbiwa added Montpellier's official website: "This (England) is a country where everybody loves football and I really want to experience this culture. It is one of the things you want to discover as a player.
"I feel I have given everything to the maximum while at Montpellier. They have been like my second family and have given me everything. There were hard times and good times but there is a very strong bond that unites us."
The centre-back will add strength to a rearguard which has struggled to keep sides at bay so far this season, and with speculation that skipper Fabricio Coloccini could leave Tyneside this month because of personal problems, his arrival could hardly come at a better time.
Yanga-Mbiwa was born in the Central African Republic but grew up near Marseille. He has won three caps for France.
He becomes the Magpies' second transfer window signing after fellow France international Mathieu Debuchy.
The deal for Gouffran was revealed by the player himself on Twitter, and the club have not yet confirmed the switch.
The 26-year-old has spent four and a half seasons with his current club but is set to join Newcastle's battle to avoid.
He wrote on Twitter: "Big thanks to everyone who has supported me through the good times and bad times. I thank the leadership of the club and the staff for helping me grow. I need a new challenge and therefore I hope that you respect my choice. I will follow all the results of the Girondins (Bordeaux). Tomorrow I will be a new player of Newcastle and I am proud. Thanks to everyone....kisses."
Their attempt to sign Loic Remy from Marseille came unstuck when QPR beat their offer.
However, Nancy full-back Massadio Haidara is also on the brink of joining the club and Toulouse midfielder Moussa Sissoko is also known to be a target.