The price of $6.3 billion will quadruple the initial investment in KEB by Lone Star.
HSBC is not expected to make an offer for the remaining KEB shares and the bank is expected to remain on the stock exchange.
HSBC chairman, Stephen Green, said: "Our stated strategy is to focus on expanding HSBC's presence in important growth economies, this positive acquisition reflects that strategy."
The deal, which is subject to government and regulatory approval, would be the second biggest in South Korea's financial sector.
However, the authorities have said that legal issues involving KEB must be resolved before it would sanction the deal.
It is alleged that a former government official conspired with a Lone Star lawyer and KEB's chief executive to inflate KEB's losses and therefore allow Lone Star to buy it for a cheaper price.
Paul Yoo, head of the South Korean unit of Lone Star, is on trial for allegedly lowering of the share price of the former credit card unit of KEB.
This led to the fund cancelling a $7.3 billion deal to sell KEB to local bank Kookmin last November.