The victory sets up a title decider against Mexico at Wembley Stadium on Saturday after the Mexicans beat Japan 3-1 in the earlier last four clash.
Brazil, whose obsession with winning gold is matched by few other countries, won with second-half goals from forward Leandro Damiao, now tournament top scorer with six, after a 38th minute opener from Romulo in front of a 69,389 crowd.
Damiao said: "I'm so happy, we have made a huge effort to reach the final. We are here to win the gold medal - it was a tough match but we are a great team. We are Brazil - we are here for the gold."
Defender Rafael, who plays for Manchester United, added: "It was an amazing feeling to be playing for Brazil on my home ground.
"We were confident, the coach was confident - and the final will be different to every other match we have played."
The pre-tournament favourites, who have been trying to win the Olympic title for 60 years, coming closest with silver in 1984 and 1988, have now won all five games at the London Olympics scoring three goals in each with a tally of 15 to 5.
South Korea caused them problems at the start and had an early penalty claim turned down when Juan Jesus's foot clumsily connected with Ji Dong-won's face in the six-yard box but, apart from a few chances from Ji, they never really threatened.
Korea now face Japan in what is likely to be a lively battle for the bronze medal at Cardiff's Millennium Stadium on Friday while Brazil will hope to be crowned Olympic champions at last against Mexico on Saturday.
The Koreans, who squeezed into the semis after beating hosts Britain on penalties, defended stubbornly until the 38th minute, showing why they had only conceded two goals all tournament.
But Korea lost the ball on the halfway line to Neymar and Brazil, who became more imperious as the game wore on, broke away with the playmaker feeding Oscar, who glided past a line of hapless defenders before finding Romulo on his right.
He planted the ball into a near-post gap with goalkeeper Lee Bum-young arriving too late to get a hand or leg to it.
Damiao capitalised on more good work by Neymar to make it 2-0 after 57 minutes and the game was settled seven minutes later when the forward took advantage of more poor Korean defending for his second and Brazil's third goal.
Brazil, who first competed in the Olympics football tournament in 1952, also have two bronze medals from 1996 and 2008.
Their resolve to win gold in London was strengthened after arch-rivals Argentina failed to qualify for the finals having won the previous two Olympics tournaments.
Mano Menezes's young side, who are expected to form the backbone of the team at the World Cup in Brazil in two years time, now have the perfect stage at Wembley - which Menezes has described as "the temple of soccer" - to end their long wait.