The 23-year-old French international is now set to fly into England next week for talks with the club's management to finalise a deal.
Sky Sports understand that the clubs have agreed an €8million (£6.7million) fee for the central defender.
Yanga-Mbiwa is one of the most highly-rated young defenders in Europe and already has three international caps to his name with France.
Newcastle have been working hard to bring in recruits this month, but thus far have only brought in Yanga-Mbiwa's international colleague Mathieu Debuchy.
Now the club have pressed ahead with a deal for Yanga-Mbiwa, after he was watched closely in recent weeks by chief scout Graham Carr.
After their failure to finalise a deal for Loic Remy, Newcastle will be desperate to push through Yanga-Mbiwa's deal.