Hendrickson was born June 18, 1896 in Juneau, Alaska, where he grew up, to Finnish immigrants. He entered politics in 1946, when he was elected mayor of Juneau, in which office he served until 1953. At the same time, he was a member of the territorial House of Representatives from 1948 to 1953.
In 1953, Hendrickson was appointed Secretary of Alaska under Governor Frank Heintzleman. He held this office until statehood, serving as acting governor twice, once in 1957 and again from 1958 to 1959. Hendrickson was the first governor born in Alaska.
He died in 1983 and is buried at Evergreen Cemetery in Juneau.