LAKE BUENA VISTA, Fla. — Lane Graves was doing what any 2-year-old boy would be doing on a hot Florida evening — splashing around in the shallow waters of a lagoon. His parents and sister, Nebraskans all, were nearby on the beach at a Disney resort here, relaxing, carefree.

Suddenly, an alligator sprang from the water and clamped its jaws around the boy. Lane’s father, Matt Graves, bounded into the lagoon to wrestle his son from the animal’s steel-trap grasp, but lost the battle, according to an account by the Orange County sheriff, Jerry L. Demings.

The alligator made off with the boy, and an intense search for him yielded nothing in the wide, murky expanse of water until more than 16 hours later, early on Wednesday afternoon, when divers found him about six feet below the surface and only 10 to 15 feet from where he had last been seen. He was placed in a marine patrol boat, covered with a white sheet, and turned over to the medical examiner for an autopsy.

During a news conference less than a mile from the lagoon, Sheriff Demings said that he and a Catholic priest had delivered the “tough message” of the boy’s death to Mr. Graves, his wife, Melissa, and their 4-year-old daughter, who live in the Elkhorn section of Omaha, Neb.

“The family was distraught but also, I believe, relieved that we were able to find their son,” said the sheriff, who noted that there was no question in his mind that “the child was drowned by the alligator.”

Lane had been splashing about, the sheriff said, despite a sign that said swimming was not permitted in the lagoon. His father also summoned a lifeguard from a nearby pool, but he, too, was unable to rescue the boy.

The medical examiner ruled Thursday that the cause of death was drowning and traumatic injuries.

In a statement on Thursday, the family expressed their appreciation for everyone involved in the search and asked for privacy. “We are devastated,” the statement said.