The 33-year-old went missing after renting a boat on Lake Piru, in Los Angeles, with her four-year-old son last Wednesday.
The local Sheriff's office said they are "confident" the body they found on Monday morning is that of the actress.
"There was no indication of foul play, no indication of suicide," Sheriff Bill Ayub said.
While formal identification has not yet taken place, he said based on the location the body was found, the physical characteristics and clothing and the fact nobody else has been reported missing meant police are confident it is Rivera's body.
They said Lake Piru park rangers found her body floating near the surface of the water in an area that is 35 to 60ft deep.
Due to the body decomposing over the five days since Rivera went missing, the body filled with gas and rose to the surface after having probably been stuck in very heavy vegetation, Sheriff Ayub added.
Divers had searched that area thoroughly before Monday without finding her, he said.
The sheriff said her son, Josey Hollis Dorsey, had told detectives the pair went swimming and she boosted him onto the deck before he looked back to see her disappear under the surface of the water.
He was discovered alone in the boat, asleep, wrapped in a towel and wearing a life jacket, by the owner of the boat rental company who was concerned after they did not return at the time they were meant to.
Josey told investigators he and his mother went swimming and he got back on the boat, but "his mum never made it out of the water," sheriff's sergeant Kevin Donoghue said on Sunday.
Sheriff Ayub said their theory is that the boat drifted as they swam and she "mustered enough energy to get her son on board, but not enough to save herself".
Her body has been flown 40 miles (64km) to the coroner's office in Ventura where a post-mortem will be conducted, authorities said.
Detectives narrowed down the search area by talking to people who were on three other rental boats at the same time as Rivera, as they told them where they had seen her at what time.