The French newspaper claims the two clubs have already agreed on a transfer fee, thought to be around €8 million.
Yanga-Mbiwa is expected to fly to Newcastle on Monday to meet with Magpies chiefs and agree personal terms with the Premiership club.
Newcastle have long been following the highly rated defender, but they only decided to make a move after captain Fabricio Coloccini expressed his desire to leave the club due to personal reasons.
Alan Pardew believes the France international will be a perfect replacement for the Argentine, and he should have no problems adapting to the new surroundings with a number of his international teammates already at St James Park.
Yanga-Mbiwa, 23, has spent his entire career at Montpellier, making 186 league appearances for the club and scoring 4 goals in the process.