Hirscher won with a combined time of two minutes 6.52 seconds over the downhill and slalom events.
The 28-year-old is regarded as one of the all-time greats in the sport with 55 World Cup race wins but had never won gold in two previous Winter Games.
Frenchmen Alexis Pinturault and Victor Muffat-Jeandet won silver and bronze.
Hirscher has previously played down the importance of an Olympic medal, saying World Cup wins were more important for his status in the sport, but afterwards said the gold was a “dream come true”, although he also said he felt “the same” as when becoming world champion.
Asked if the gold medal cements his legacy as one of the sport’s greats, he added: “For sure. I’m super-happy because now this stupid question is gone away.
“If I’m thinking that my career is perfect without a gold medal, now this question is zzz, deleted.”
Hirscher was well placed for gold after a 12th-placed finish in the downhill, his less favoured of the two events, and clinched the win with the fastest time in the slalom.
Muffat-Jeandet produced a brilliant slalom run, just a 0.01 seconds slower than Hirscher, to take bronze despite sitting 29th after the downhill.
Hirscher’s previous Olympic best had been silver in Sochi in the slalom, but he now has another three realistic medal opportunities to come in these Games in the slalom, giant slalom and super G.
He has had a remarkable season during which he has become the second most-decorated male skier of all time by winning six of the eight slalom races he has competed in, despite breaking an ankle in August.
The Austrian has also won the overall World Cup crown in each of the last six seasons and has a comfortable lead in the current campaign.