Purvis Virginia Parker, 11, and Quadrevion Henning, 12, were last seen on the afternoon of March 19 when they asked Quadrevion's grandfather if they could play basketball at the nearby park.
The bodies were found in the park lagoon on Friday.
"Yes, it's my son," said Angela Virginia, who said she identified Purvis from a photo that police showed her. She said Quadrevion was identified by his family.
Police did not immediately confirm the identities.
"Honestly I don't think there was any foul play," said Dennis Frazier, Quadrevion's uncle. "That makes it kind of nice for the family that they weren't held against their own will."
Autopsies are being preformed Saturday and police scheduled a news conference for later in the day.
Frazier said family members had identified Quadrevion from a photo that police showed them. Angela Virginia said she also identified her son, Purvis, from a photo.
The first of the two bodies was found about 7:30 p.m. Friday after a man and his son walking in the park saw something floating, Police Chief Nan Hegerty said.
Police and Fire Department divers found the second body around 10 p.m. Both bodies were fully clothed, had been in the lagoon from quite some time and were bloated, authorities said.
"It's not a young child, and it's not an adult," Hegerty said. "It's somewhat decomposed. It's very difficult at this early time to make any indication of who the child might be."
After the boys' disappearance, police and volunteers searched the neighborhood, posted leaflets around the city and made repeated appeals for information anyone might have.
Divers had waded through the lagoon's icy water, but because of the muddy bottom, it was possible the bodies could have been missed in a search, Hegerty said.
The boys' families said the two had no history of running away and had good school attendance records, and police fielded hundreds of calls on a tip line offering possible leads.
Police spokeswoman Anne E. Schwartz complained last month that they didn't have substantial leads despite hundreds of phone calls to a tip line. In addition to the door-to-door searching, officers used dogs and thermo-imaging equipment to look for the boys, Schwartz said.
The department frequently gets reports of missing children, but they typically have a history of running away and turn up quickly, she said. The two boys do not have a history of running away.
A Florida group called A Child Is Missing also had helped police in the search. The group called all home and business telephone numbers within a mile of where the boys were last seen and played a recorded message about the pair, officials have said.
The National Center for Missing and Exploited Children and America's Most Wanted also posted pictures of the boys on their Web sites.