Hands, who was suing Citigroup for £1.5bn over allegations that the bank had misled him during the bidding process for the music company, had taken his case to London's high court last week, but dropped it on Friday.
A statement from Citigroup, which noted that the bank "very pleased" that the allegations had been dropped, revealed that Terra Firma had also agreed to pay Citigroup's costs.
Terra Firma has declined to comment further on how much the collapsed case would cost Hands in legal bills, but the Sunday Times has reported that it could be nearly £20m.
Terra Firma bought EMI, known for representing artists such as The Beatles, for £2.4bn in 2007. However, the music company struggled to the extent that Citigroup eventually stepped in and took control of EMI in 2011.
Hands said in a statement issued at the time the case was dropped:
These claims were brought in good faith. However, it has become evident that our documentation of the fast-moving and complex events, and memories of these events after nine years, are no longer sufficient to meet the high demands of proof required for a fraud claim in court.
The matter is now closed. Terra Firma is looking to the future. We have an exciting portfolio of companies, a talented and experienced team, supportive and loyal investors and one billion euros of capital to invest.
Before bringing his case to the High Court, Hands tried to sue Citigroup in the US. The jury found in favour of the bank, but the verdict was later overturned on a technicality.