Police will name drifter Ottis Toole, a convicted pedophile who died in prison in 1996, as the boy's suspected killer, a law enforcement source told CNN.
Toole twice confessed to killing the boy -- and twice recanted his story, saying he made it up. It could not be learned what, if any, new evidence exists.
Hollywood police chief Chad Wagner plans to provide details at an afternoon news conference. He will be joined by the boys parents, John and Reve Walsh.
John Walsh is host of the television show "America's Most Wanted." His son would now be 33.
Adam disappeared from a Sears store across from the Hollywood police station on July 27, 1981. Two weeks later, his severed head was found in a canal 120 miles away. The boy's body was never recovered.
Toole died in a prison in 1996, while he was serving a life sentence on unrelated charges. He was never charged in the case, nor was anyone else.
Toole's confessions in the Walsh case were always questioned by police, because Toole confessed to other murders that police knew he did not commit.
Although the details of his story changed, Toole did lead police to the Sears store and pointed out the spot where Adam was last seen. He also led police to the canal where the boy's head was found. But investigators could not find Adam's body where Toole said he left it.
A bloody piece of carpet removed from Toole's car was lost by police many years ago -- before DNA testing became available.
Police believe a 17-year-old security guard asked a handful of rowdy kids who were playing video games in the toy department to leave the store. Investigators believe Adam was grouped in with those kids, who left him alone outside the store. That was the last time he was seen.
Walsh told CNN's Larry King in 2007 that he believes Toole was responsible for his son's death.