The victory sets them up for a title decider against Mexico at Wembley on Saturday after the Mexicans beat Japan 3-1 in the earlier semi-final in London.
Brazil, whose obsession with winning the Olympic gold is unmatched by few other countries, won with two second-half goals from Leandro Damiao, now the tournament's top scorer with six goals, after a 38th minute opener from Romulo in front of a 69,389 crowd at Old Trafford.
The pre-tournament favourites, who have been trying to win the Olympic title without success for 60 years, coming closest with silver medals in 1984 and 1988, have now won all five games scoring three goals in each of them with a tally of 15 to 5.
South Korea caused them some problems at the start and had an early claim for a penalty 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, Korea never really threatened.
They now face Japan in what is likely to be a lively battle for the bronze medal in Cardiff's Millennium Stadium on Friday (1845 GMT) while Brazil will hope to fulfil their date with destiny against Mexico on Saturday (1400 GMT).
Korea, who squeezed into the last four after beating hosts Britain on penalties in the quarter-finals, defended stubbornly until the 38th minute, showing why they had only conceded two goals all tournament.
But after losing the ball on the halfway line to Neymar, Brazil, who became more imperious as the game wore on, broke away with Neymar 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 goalie Lee Bum-young too late to get a hand or leg to it.
Leandro Damiao capitalised on good work by Neymar to make it 2-0 after 57 minutes and the game was settled seven minutes later when he took advantage of some more poor Korean defending for his second and Brazil's third.
Brazil first competed in the Olympics in 1952 and have picked up two bronze medals, in 1996 and 2008, to add to their silvers.
Their resolve in winning gold in London was strengthened after their arch-rivals Argentina failed to qualify for these finals after winning the previous two Olympics.
Mano Menezes's young side, who are likely 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.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sports and on Facebook at AhramOnlineSports)