The gains also reflected growing confidence in South Korea's economy, after data on Tuesday showed positive export growth and slowing consumer inflation. The reports were welcomed by a market already betting on a recovery in domestic demand.
The benchmark Korea Composite Stock Price Index (KOSPI) rose 2.66 percent to end at 1,188.95, its biggest percentage gain in a single session since advancing 2.92 percent on October 28, 2004.
It was also the market's highest close since ending at 1,190.17 on October 14.
"Kookmin's earnings were very strong. Banks have shown the best improvement in earnings this quarter among major sectors," said Chang In-whan, chief executive and fund manager at KTB Asset Management.
Kookmin Bank rose 10.82 percent to end at 63,500 won after it surprised investors late on Monday by posting a third-quarter net profit well above market estimates.
Kookmin, which says one in two South Koreans is a customer, hit the daily limit of 15 percent at one point, adding as much as $2.7 billion to its market value.
Shinhan Financial Group surged 5.46 percent to 36,700 won. The country's second-biggest banking group said after the market's close its net profit rose 26 percent from a year earlier, topping market estimates.
Hyundai Motor Co, the country's top auto maker, surged 4.05 percent to 79,700 won after it said sales in October hit a record.
The car maker had been lifted earlier by positive October exports data and after Wall Street gained overnight amid falling oil prices and optimism about the US economy.
Samsung Electronics Co Ltd rose 2.17 percent to 564,000 won, while Hynix Semiconductor Inc gained 2.62 percent to 19,550 won.
Korean Air Co, the country's top carrier, surged 5.9 percent to 20,550 won amid eased worries over fuel costs.
LG Telecom Ltd rose 3.69 percent to 5,340 won after it said third-quarter net profit topped analysts' expectations.
Trade volume reached some 424.5 million shares worth 4.2 trillion won compared with 320.5 million shares worth 2.6 trillion won on Monday. Gainers more than doubled decliners by 534 to 214 with 64 titles ending flat.
Institutional investors sold a net of 3.7 billion won, data at 0645 GMT showed, while retail investors sold a net of 182.5 billion won.
The December KOSPI 200 futures index advanced 4.90 points to 153.40, while the underlying KOSPI 200 spot index added 4.14 points to 152.98.
South Korea's junior and tech-heavy Kosdaq market rose 1.25 percent to finish at 594.82.