The 23-year-old came through a medical on Tyneside on Tuesday after the clubs agreed a fee last week, and Montpellier have confirmed the player's exit after playing 219 games for them.
Yanga-Mbiwa told 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.
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 and Bordeaux striker Yoan Gouffran are also known to be targets.