The move follows the surprise departure of Damian Darragh, regarded as a star manager at Terra Firma, which is controlled by financier Guy Hands.
Mr Darragh had been due to head up the fund alongside six other people.
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Mr Kinski, a former executive at ScottishPower succeeded founder Brian Souter at Perth-based Stagecoach in 1998. He lasted just two years having endured a set of profit warnings in the wake of its £750 million acquisition of Coach USA.
But he has since built a career over 14 years at Terra Firma, where he is operational managing director.
He has been involved with a number of its investments including chairing wind power company Infinis before its stock market listing last year. He remains on its board.
Terra Firma said that it had asked Mr Darragh to leave after a review which is understood to have considered his fundraising and leadership skills.
It turned to Mr Kinski, who had both fundraising and corporate management experience to serve alongside recent hires Stefan Thiele and Ingmar Wilhelm in jointly leading its renewable energy infrastructure team.
"Mike, Stefan and Ingmar have outstanding financial, operational and transactional skills," Terra Firma said.
Mr Kinski joined Terra Firma in 2000 after leaving Stagecoach. He had previously been chief executive of power distribution and water operations for ScottishPower.
Mr Hands and Mr Darragh were colleagues at Japanese bank Nomura before founding Terra Firma in 1994.