Knight was born in Provo, Utah, but his family moved to Los Angeles when he was a boy. His father, Jess Knight (son of Jesse Knight), was a mining engineer, but Goodwin followed in his mother's (Lille) father's (John B. Milner) footsteps. This grandfather was a judge in Provo, Utah.
Knight attended high school in Los Angeles, at Manual Arts High School. One of his classmates was Jimmy Doolittle. He earned an A.B. in Law and Business from Stanford University, where he was a member of the Stanford Chaparral, in 1919. Knight also attended Cornell University. He served in the U.S. Navy during World War I.
Knight was a judge of the Superior Court in Los Angeles beginning in 1935. He was reelected in 1936 and 1942 without significant opposition. His case load varied from the glamorous to the mundane. He oversaw weddings and divorces for Hollywood starlets.
Knight began his political career in 1944, when he pursued the Republican nomination for the U.S. Senate. He bowed out early, though, to back Fred Houser. He was elected as the Lieutenant Governor under Earl Warren in 1946 then reelected in 1950. He became governor himself when Warren resigned to become Chief Justice of the United States in 1953.
As governor, Knight fought for control of the Republican Party of California with U.S. Senate Majority Leader William Knowland and Vice President Richard Nixon. In 1954, Knight was easily elected to his own full term. At first Knight seemed to make an alliance with Knowland, but this began to sour in 1956 when Knowland supported Nixon for renomination as vice president. In 1957, Knowland announced that he would challenge Knight in the 1958 Republican primary for governor. Knight, known as a moderate, and sympathetic to organized labor, faced a serious threat because the Republican Party was growing more conservative. He was induced by Knowland, Nixon, President Dwight Eisenhower, and others to run for Knowland's Senate seat instead of running for governor again. Both Knowland and Knight went down to defeat in 1958, with Knowland losing the gubernatorial race to Edmund G. "Pat" Brown, Sr. and Knight losing the Senate race by over 10% to Clair Engle, severely weakening the California Republicans. This left Nixon in control of the California party and in line for the presidential nomination, which Knowland and Knight had also desired.
In 1964, Knight endorsed Nelson Rockefeller for the Republican nomination against Barry Goldwater. Rockefeller was unsuccessful in stopping Goldwater, the darling of the party's growing conservative wing. Knight never ran for political office again.
Knight's first wife, Arville, died of a heart attack on October 29, 1952. He and Arville had two daughters. He married Virginia Carlson on August 2, 1954 at the Episcopal Church of Our Savior in Los Angeles. Virginia Carlson's first husband, Lt. Lyle Carlson, was killed in action in World War II. Knight died in Inglewood, California in 1970, and was buried in Rose Hills Memorial Park in Whittier.