Timothy McGuirk, a spokesman for the Massachusetts Executive Office of Public Safety and Security, told the media that the cause of death was ruled as drowning and the manner of death was determined to be an accident.
Campbell's body was recovered from a lake on the island in late July. Campbell, 45, was the subject of a two-day search after a paddleboarder was seen to struggle and go under the water in Edgartown Great Pond near a home owned by Obama last month.
The Obamas were not present at the time of his death, state police said.
Campbell had been a sous chef at the White House and came to work for the family after Obama completed his second term in 2017, the former president and his wife, Michelle Obama, said last month.
The chef, who lived in Dumfries, Virginia, leaves behind his wife, Sherise, and twin sons.
(Reporting by Kanishka Singh in Washington; Editing by Andy Sullivan)
By Kanishka Singh
