The funding is part of a £200m lending facility launched in partnership with the UK Green Investment Bank (GIB) earlier in November 2014.
The Sròndoire wind farm, which will feature three turbines, is a joint venture between the Lithgow family of Ormsary and the Broadfoot family of Stronachullin.
The project will be partly owned by the local community, allowing it to have commercial benefits.
KKR co-head of credit Nat Zilkha said: "Non-bank lending is becoming an increasingly important source of capital for many businesses and sectors. We have deployed almost $5 billion globally via our different lending platforms.
"This is KKR’s first investment in the UK renewable energy sector as renewable power becomes a crucial part of the UK’s energy mix."
GIB and KKR have agreed to provide up to £100m to the lending programme, which will be managed by Temporis Capital.
The bank secured approval from the European Commission in May 2014 to expand its investment mandate to include community-scale renewables, particularly small-scale hydro-electric and onshore wind projects.
The funding represents KKR’s first investment in UK renewable energy market.
KKR had earlier invested in renewable energy globally including the US, Mexico, Australia, France, Italy, Spain, Portugal, and South Africa.
