Grainger will succeed Rod Carr at the national funding body in July, having retired from rowing last year as Team GB's most decorated female Olympian.
The 41-year-old was a gold medallist at London 2012 and won silver at four other Games from Sydney 2000 to Rio 2016.
The appointment was confirmed by the department of culture, media and sport on Friday evening, having been made by culture secretary Karen Bradley and approved by Prime Minister Theresa May.
The department had until midnight to finalise its decision, with Saturday signalling the start of purdah - the pre-election period during which such matters are put on hold.
"I am absolutely thrilled to be appointed as the next UK Sport chair," said Grainger.
"I am also very honoured to be joining the team at UK Sport and building on the success and commitment to excellence that I have witnessed and enjoyed as an athlete. I'm also acutely aware of the many challenging issues currently within sport and I hope to play a role in addressing them."
Sports minister Tracey Crouch added: "Dame Katherine is a peerless leader both on the water and off it. As one of our greatest ever Olympians, she has an outstanding understanding of high performance sport, and through her educational and charity work has a proven commitment to inclusion.
"I know she will be an inspiring chair of UK Sport. I would also like to thank outgoing chair Rod Carr for his superb work at the helm of UK Sport over the past four years."
Carr will step down on April 22 after four years as chairman, with board member Lis Astall taking over as interim chair until Grainger begins work on July 1.
It is understood Grainger was encouraged to apply for her new position, which carries a modest £40,000 salary, despite lacking administrative experience.
Chief among her most pressing concerns will be managing the protracted fall-out from the scandals surrounding British Cycling, with an independent review into the culture and environment of the body long overdue for publication.
Additional reporting by the Press Association.