EMI, which earlier this year rejected a proposal from Warner Music Group (WMG), said that Terra Firma's offer was the best among a number of proposals it received.
"The global music industry is undergoing significant change and, whilst EMI is confident in its ability to deliver its recently announced restructuring plans, significant uncertainty exists as to the timing and extent of future market developments," said EMI Chairman John Gildersleeve.
"Terra Firma's offer is the most attractive proposal received and delivers cash now, without regulatory uncertainty and with the minimum of operational risk to the company," he added.
EMI's shares soared on the news, which was made just before the closing bell on the London Stock Exchange. The stock finished 8.5 percent higher at $5.30.