The Belgian finished the final power stage 12.6 seconds clear of six times world champion Ogier, who ended up 1.7 ahead of third-placed Toyota team mate Elfyn Evans.
It was Neuville's first win in Monte Carlo, with the Belgian runner-up last year when Ogier won for Citroen.
Welshman Evans had led overnight with the top three separated by just 6.4 seconds but Neuville won all four of Sunday's slippery asphalt stages in the French Alps to go from third to first.
Neuville took five bonus points by winning the final power stage, 0.016 faster than Frenchman Ogier.
M-Sport Ford's Finnish driver Teemu Suninen took three bonus points for third in the stage, Evans two for fourth and M-Sport's Esapekka Lappi one for fifth.
Estonia's world champion Ott Tanak, who switched from Toyota to Hyundai at the end of last season, crashed out of the rally on Friday. (Reporting by Alan Baldwin in London, editing by Giles Elgood)