Hammond police said a volunteer kayaker, later identified as 33-year-old Eric Smith of Hobart, found a body in the river just after 8:15 p.m.
Smith, a local truck driver and avid fisherman, said he located the boy's body about 300 feet west of where Carter went missing.
"We were hoping for a good outcome, you always believe in the best, but we are just grateful that we are able to bring him home," said Veronica Collier, great aunt.
On May 21, in coordination with multiple agencies, including the Little Calumet River Basin commissioner, the decision was made to temporarily stop the flow of water into the Little Calumet River in an attempt to get as deep into the river as possible to search for Carter, police said in a news release early Tuesday morning.
The damming process had never been done before, officials said later Tuesday.
RELATED: Boy, 12, with autism last seen on video leaving Hammond hotel; search moves to nearby neighborhoods
Police said after Smith called it in, a dive team responded and removed a body from the water.
The Lake County Coroner's Office in Indiana confirmed the body belonged to Carter later Tuesday.
The heartbroken family took the news with grace. Many volunteers who helped in the search have had an emotional experience.
"This is a baby; he's autistic, special needs, who wouldn't?" one woman said. "Anybody that has a heart and loves kids, children, or have children of their own, even ones that (are) autistic, special needs, out here, trying to help."
Smith was another volunteer who never gave up.
On Monday afternoon, he got off work, got into his kayak and made several passes on the river.
After five hours, Smith made the heartbreaking discovery. He dropped in a fisherman's buoy to mark the spot, and called police.
"I looked at it because if it was my daughter I would want somebody out there giving their all, but I kept thinking it was a lost kid, and we gotta find him," he said. "It hit me so fast. When I looked down and seen him, it hurt me. I was crying before I even got back to land."
Carter disappeared at around 12:30 p.m. on May 15 from the Best Western hotel on 179th Street in Hammond.
Carter had autism, and was nonverbal, but highly functional. He lived in Kansas City, Missouri, and was in the area to visit relatives when he disappeared.
RELATED: Search continues for boy, 12, with autism last seen on video leaving Hammond hotel
Some of his family members are too upset to speak, but others offered words of grace and thanks.
"We can't thank the volunteers enough who came out here day and night calling out to Kyrin," Collier said. "Though our hearts are heavy right now, our spirits are uplifted from the outpouring of support that everyone. We can't thank you enough, and on behalf of the family, the Duckworth family, Kyrin Carter, we want to say thank you."
Volunteers have been coming by the river Tuesday, leaving flowers.
Melissa Clark from Portage came with her two kids.
"It was just me and my kids, kind of like some closure I suppose, closure on it because when I heard last night I didn't sleep," she said. "I didn't get any sleep, and I know that a lot of people around here feel the same way."
A camera in the back of the hotel captured an image of Carter as he left. And video from nearby businesses showed him running toward the river and its steep bank, Hammond Mayor Thomas M. McDermott Jr. said. Carter had run down to the river the day before he disappeared, as well, but was caught, the mayor said.
The search had continued for 10 days up until this point, as the boy's family appealed to the public for help.
Dogs, dive teams, helicopters, horses and teams of volunteers searched the area near the hotel, including the Little Calumet River.
Dogs apparently picked up a scent near the river behind the hotel, and search crews concentrated their efforts there, but the water was murky and cold, McDermott said.
The Hammond Police Department held a press conference to talk about the case at 11 a.m. Tuesday.
WATCH: Hammond officials give latest on recovery of missing boy's body
The mayor extended condolences to Carter's family, and said he was glad officials could provide some closure.