Kamil Zielnik had vanished three weeks before his body was found by a member of the public on Sunday morning.
He had been living in a tent at the side of the river.
Emergency services were called to Rose Kiln Lane where Royal Berkshire Fire and Rescue's water crew based at Caversham Road Station, retrieved the body.
The 35-year-old was pronounced dead at the scene.
A spokesman for Thames Valley Police said: "Identification has taken place of a body found in the River Kennet in Reading on Sunday.
"The body has been identified as being that of missing person Kamil Zielnik.
"The death is currently being treated as unexplained, but is not believed to be suspicious."
A file was due to be passed to the Berkshire Coroner for an inquest to be opened.
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