Wilkinson, who was 94, died in Del Mar, Calif., last week. The cause of his death wasn't disclosed.
Wilkinson received his commission in 1940 and reported to the heavy cruiser USS Louisville for his first tour of duty.
He graduated from the Naval Submarine School in Groton in March 1942. During World War II, he participated in eight submarine war patrols.
Wilkinson commanded the Nautilus, which was commissioned in 1954 as the world's first nuclear-powered ship. On Jan. 17, 1955, he ordered all lines cast off and signaled the message, "Underway on nuclear power."
The Submarine Force Library and Museum said on its Facebook page that delivering the message was not a simple matter. Wilkinson said two Navy captains who handled public relations advised him he was about to take part in a historic event and he should send a "historic message."
"'Listen,' I replied, 'we're doing our part getting ourselves, the ship and its systems checked out and ready,'" the museum quoted Wilkinson as saying. "'You gentlemen are public relations experts. Write a historic message, and we'll send it.'
"That took care of them for a day and a half," he said. "Then they gave me a message that was one and a quarter typewritten pages long with some elegant-sounding words."
Instead, Wilkinson said, he wrote the briefer message.
Wilkinson was born in Long Beach, Calif., on Aug. 10, 1918. After attending the Naval War College in Newport, R.I., in 1957-58, he served as commander of a submarine division.
In September 1961, he was assigned as the initial commanding officer of the first nuclear-powered surface ship, the guided missile cruiser Long Beach. He was director of the submarine warfare division from 1963 to 1966.
Wilkinson served as executive officer in three submarines: the Menhaden, the Raton and the Cusk, which was the first submarine to fire guided missiles. And he commanded four submarines: the Volador, the Sea Robin, the Wahoo and the Nautilus.
Wilkinson retired from the Navy in 1974 as a vice admiral and later was executive vice president of Data Design Laboratories, a high-tech company. In 1980, he became the first president of the Institute of Nuclear Power Operations.
His wife, Janice Wilkinson, died in 2000. He is survived by four children and four grandchildren.
Copyright 2013 The Associated Press.