Police said divers made the discovery in the River Calder, in Huddersfield, West Yorkshire, on Saturday evening after they were alerted earlier in the morning.
The men have been named locally as Martin Andrews and his teenage son Jack, according to the Huddersfield Daily Examiner.
Officers were called at 11.20am after a passer-by saw personal belongings, including clothes, a mobile phone, a camera and a set of car keys by the waterside which had been there for about 50 minutes.
West Yorkshire Police said officers located a car parked near the Pudsey area of Leeds, where a woman confirmed her 43-year-old husband and his 19-year-old son had gone magnet fishing at 6.15am.
A police spokesman said divers were called in following an extensive search of the area and there being no trace of the two men. He said the divers located the bodies at 7.22pm.
“The family are aware and inquiries are ongoing into how they ended up in the water,” he added.
A dog walker who reportedly found the pair’s belongings told the Huddersfield Daily Examiner she “thought there was something not right”.
“I had a quick look to see if there was anyone about but I couldn’t see anyone,” she said. “I left it for half an hour or so and called the police. Stayed at the site until they arrived.
“The currents in this area can be really, really strong and there’s no life-saving equipment here.
“It’s heart-breaking whats happened. I feel so sorry for his family. That poor woman, and for it to happen on Father’s Day makes it even worse.”