The 22-year-old has put pen to paper on a six-year deal which will keep the Frenchman at St. James' Park until the summer of 2025.
Saint-Maximin will wear the number ten shirt for United and could make his bow for the Magpies in Saturday's pre-season friendly against Ligue 1 side Saint Étienne - the club he made his senior debut for at the age of 16.
Head coach Steve Bruce said: "I'm delighted to bring Allan to St. James' Park. He is a very talented young player with a big future ahead of him.
"He has all the attributes you would want in an attacking player, including lightning pace, so I'm sure he'll excite everybody. He is a great addition to Newcastle United and the Premier League."
After joining AS Monaco in 2015, Saint-Maximin experienced loan spells with Bundesliga side Hannover 96 and French club SC Bastia before making the switch from Les Monégasques to join Nice in the summer of 2017.
With 100 Ligue 1 appearances already to his name and seven caps for France Under-21s, Saint-Maximin has also featured in the Europa League for Nice, scoring twice in four games during the Eaglets' 2017/18 campaign.