The capital injection will help U.S. wind energy business Everpower finance its development pipeline, the companies said, without disclosing financial details.
"We see significant investment potential in the fast growing U.S. renewable energy market, and Everpower has both a strong management team and an attractive portfolio of projects," Terra Firma Chairman Guy Hands said in a statement.
U.S. President Barack Obama has kept energy reform high on his priority list since taking office in January, providing incentives for wind energy development.
The deal was worth around $350 million, a source familiar with the situation said. Terra Firma was advised by Morgan Stanley and Climate Change Capital.
Terra Firma has bought the business from renewable energy fund Good Energies and the Everpower management team, both of which are re-investing alongside Terra Firma.
The deal is only Terra Firma's second since its ill-fated 4 billion pound (US$6.54 billion) buyout of music business EMI at the height of the buyout boom in 2007.
The ailing music group accounted for the vast majority of Terra Firma's 1.37 billion euro (US$1.96 billion) writedowns this year, and Terra Firma was forced to inject extra capital into EMI twice in just six months.
Everpower owns a newly constructed project with a 62 megawatt output and has a near-term development pipeline to provide over 800 megawatt of power.
Its business is concentrated in the North East and West Coast power markets which benefit from stronger prices and available transmission, Terra Firma said.
Terra Firma bought Australia's second-largest beef producer Consolidated Pastoral Company in March this year from gaming industry boss James Packer, the son of the late media mogul Kerry Packer.
That deal was valued at around 425 million Australian dollars (US$356.2 million) and partly financed by Rabobank, according to media reports.