Her room window had been smashed to pieces and the lifeless body of a man was found on the ground outside her hotel.
Mitchell worked for BBC Media Action, the organisation’s charitable arm.
Nairobi police chief Augustine Thumbi said: “We are investigating circumstances surrounding these deaths, but so far it is apparent the man jumped (out of) the window after killing her.
“We do not know the motive so far, and these are things the investigators are trying to put together.”
A spokesman for the BBC said Mitchell was a “much-loved” member of the team who had worked for the corporation for 14 years.
BBC Media Action CEO Caroline Nursey said: “We are all shocked and horrified by this terrible news.
“Kate was a much-loved member of staff…she was well known across our whole organization, especially by our teams in Ethiopia, South Sudan, Zambia, and London.
“We send our deepest condolences to her family and her many friends around the world.”