The benchmark Korea Composite Stock Price Index (KOSPI) closed up 0.47 percent at 988.71, its best finish since ending at 1,059.04 on January 4, 2000.
LG Electronics, the world's biggest maker of air conditioners, jumped 7.07 percent to end at 80,300 won and LG Corp surged by its daily permissible limit of 15 percent to close at 28,950 won.
"Presumably Sovereign will be vocal in helping improve corporate governance and transparency at the LG units," said Thomas Choi, head of research at PCA Asset Management.
"This is going to help Korean management wake up and realise they cannot screw minority shareholders as they did before."
LG Group's telecom units Dacom Corp and LG Telecom Co Ltd rose 15 percent and 5.42 percent respectively.
Sovereign, which has been leading a push to shake up management at top South Korean oil refiner SK Corp, said it did not intend to change management at the LG Group, the country's second-biggest conglomerate.
Shares in SK Corp, in which Sovereign is the second-biggest shareholder, climbed 3.2 percent to 58,000 won.
Sovereign's LG investments come ahead of a controversial SK Corp shareholder meeting in March over managerial control.
"The purchase of stakes in LG could help Sovereign win over investors in its dispute with SK Corp, as it could signal they are not just corporate raiders and that they intend to be long-term investors," said Kim Hyun-tae, a fund manager at Woori Investment Trust Management.
Other telecom shares ended lower, with SK Telecom Co, South Korea's top mobile operator, falling 0.28 percent to 179,000 won, and top local fixed-line and broadband provider KT Corp down 1.32 percent at 41,250 won.
South Korea's Minister of Information and Communication Chin Daeje told Reuters in an interview the government would not cut mobile phone charges this year after reducing them 3.7 percent in 2004.
Trade volume reached 628 million shares worth 4.5 trillion won compared to 540 million shares worth 3.5 trillion won on Friday. Gainers edged out losers by 527 to 241 with 45 titles ending flat.
Foreign investors bought a net of 186.1 billion won ($181.4 million) in shares on the main bourse and retail investors bought a net of 342.3 billion won. Institutional investors sold a net of 418 billion won.
The March KOSPI 200 futures index rose 0.25 point to 127.60 and the underlying KOSPI 200 spot index gained 0.66 point to 128.09.
The over-the-counter Kosdaq fell 0.40 percent to finish at 508.61.