Scott McGuire, 41, was found dead in the River Clyde at around 8.15am on July 8.
The man had been sleeping rough near a bridge that crosses the river at Calton Place in Glasgow, Police Scotland said.
The force said two men, aged 38 and 32, and a 30-year-old woman have been arrested in connection with Mr McGuire's death. They are expected to appear at Glasgow Sheriff Court today.
A report will be sent to the procurator-fiscal.