Normal operations at the airport were interrupted briefly but have resumed, the airport said.
Alaska Airlines confirmed the aircraft belonged to its subsidiary Horizon Air and was a Bombardier Dash-8 (Q-400) turboprop aircraft that likely had no passengers on board.
The Pierce County Sheriff's Department said the crash was not a terrorist incident, and the man who piloted the Alaska Airlines plane was a 29-year-old "suicidal male" who lived in Pierce County.
"Our hearts are with the families of the individual aboard as well as all of our Alaska Air and Horizon Air employees", said Constance von Muehlen, the airline's chief operating officer.
The Q400 is a twin-prop aeroplane with up to 78 seats, depending on configuration.
The plane was allegedly "flying around Puget Sound", before later reports indicated there was a "large smoke plume" at Ketron Island. "No others involved", Sheriff's Office said.
Mr Troyer said that he is working with Federal Bureau of Investigation and military personnel as they investigate what happened. Eventually the plane crashed in a remote wooded area of Ketron Island in Puget Sound, leaving behind a fiery pile of debris.
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"The person who stole it was either doing it on a lark, or was suicidal", Pastor said, adding there was no indication anyone else was on the plane.
Witness footage shows the plane's erratic flight prior to the crash.
SeaTac confirmed the plane crashed after being piloted by an employee.
Jenkins described the island as remote, dark and sparsely populated. Police also said the incident was not related to terrorism.
"We're just trying to find a place where you can land the plane safely", the controller says.
"Told F-15s made it within a few minutes of theft of plane". "Saw two fighter jets fly overhead then smoke".
According to the Seattle Times, air traffic control, who referred to the man by what is believed to be his first name, tried to encourage him to land.
This is a developing story and will be updated as more information becomes available.