Born in McKenna, Washington, Goodwin received a Bachelor of Arts degree from Washington State College in 1931 and a Bachelor of Laws from the University of Oregon School of Law in 1934.
He was in private practice in Tacoma, Washington from 1940 to 1964, also serving as a United States Marine Corps Private First Class during World War II, from 1944 to 1945, and becoming a member of the Board of Regents of Washington State University from 1957 to 1975.
He was the United States Attorney for the Western District of Washington from 1964 to 1966.
He was confirmed by the United States Senate on April 21, 1966, and received his commission the same day.
He served as Chief Judge of the Eastern District from 1972 to 1973 and as Chief Judge of the Western District from 1973 until his death on December 31, 1975, while playing tennis in Tacoma.