The body of Ian Turton was recovered in the river between Sangam-Mekedatu stretch, around 100 km from Bangalore, Ramangara District Superintendent of Police Anupam Agarwal said.
A search was on to locate Turnton's friend Mike Eastern, he said.
The duo had been missing since May 19 after they went on the river rafting from Muthathi in Mandya District.
Following a complaint, police mounted a search and traced the boat on May 23 at a location between Sangama and Mekedatu, known to be infested by crocodiles.