Olympic champion Odermatt, winner of four of the six men's World Cup giant slalom events this season, clocked a winning aggregate time of 2min 34.08sec over two testing runs down a super-icy L'Eclipse piste.
His Swiss teammate Loic Meillard (26) took silver, 0.32sec adrift, while Austrian Marco Schwarz (30), who won alpine combined silver last week and set the fastest time in the first of two legs, claimed bronze (+0.40).
Odermatt, who won the downhill world title last Sunday for his first career world championships medal, became the fifth man to win the downhill and the giant slalom at the same world championships after Zeno Colo (1950), Toni Sailer (1956, 1958), Jean-Claude Killy (1968) and Aksel Lund Svindal (2007).
He also becomes the first Swiss racer to win multiple titles at a single edition of the world championships since Pirmin Zurbriggen in 1987 (super-G, giant slalom).
France's defending world champion Mathieu Faivre (31) finished 4.49sec off the pace in 19th spot after managing just 25th fastest in the first run.
Italy's Giovanni Borsotti (32) took an early lead on the second run, but France's Alexis Pinturault (31), 11th fastest in the first leg, delighted the home fans when he streaked down and into first place.
Pinturault, who won gold in the alpine combined and bronze in the super-G on the same slope, is a Courchevel native and was greeted like a hero by raucous, flag-waving fans in the sun-kissed stands.
Then it was time for the top eight to muster, and they did not disappoint in a high-octane spectacle on the gruelling hill.
First Croatia's Filip Zubcic (30), then Norway's 2019 world champion Henrik Kristoffersen (28) and Austrian Stefan Brennsteiner (31) all bettered the leading time.
Brennsteiner's teammate Manuel Feller (30) skied out with the line in reach, leaving the top four from the first leg to come.
Switzerland's Meillard positively tore out of the start hut, laying down the fastest second run of the day to snatch the lead by 0.44sec to pile the pressure on the top three.
Slovenia's Zan Kranjec (30), who won silver behind Odermatt at last year's Beijing Games, paid the price for going wide on a number of turns high up the course, eventually finishing sixth, one place ahead of Pinturault.
That left Meillard's teammate Odermatt, who started with a -0.55sec deficit, the Swiss making the most of his first-leg advantage to take a 0.32sec lead at the top of the leaderboard.
All eyes then turned on defending world bronze medallist Schwarz, who carried over a 0.58sec advantage from the opening run.
But his bid to become the first Austrian since Marcel Hirscher (in 2017) to win the discipline and also become the first Austrian to bag a gold at these world champs came undone.
Two crucial mistakes saw the Austrian lose ground. Watching closely as Schwarz's time showed up as the third fastest, Odermatt roared a cry of approval and hugged Meillard with glee in the finish area.
Norway's Aleksander Aamodt Kilde (30), winner of two silvers in Courchevel, skied out of the first run.
