The Ligue 1 club confirmed earlier on Tuesday that they had come to an agreement with the Tyneside club over the France international's switch and he has now passed a medical and agreed personal terms.
Yanga-Mbiwa will wear the No.13 shirt and is eligible to make his Toon debut against Aston Villa next Tuesday.
"It is an honour to be able to come to Newcastle United and have the chance to play in the Premier League," the centre-back told the Magpies' official website.
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"I have experienced a lot of positive things so far in my career and one of those is joining this club."
The Magpies have been fretting over defensive cover in recent weeks with Fabricio Coloccini keen to move back to Argentina due to personal reasons.
Newcastle manager Alan Pardew added: "We needed to strengthen the team and bringing in Mapou will give the whole squad a boost.
"He is precisely the sort of player we've been looking to bring to the club. He is a good age for us but has plenty of experience at club and international level.
"Mapou is a talented footballer, good in the air and on the ground and has all the attributes to succeed as a quality defender in the Premier League. He's a good character, too, and that will be important for us over the next few months."