Born in Baker County, Oregon to Danish parents, Poulson attended Oregon State University for two years before marrying Erna June Loennig on December 25, 1916. The couple arrived in Los Angeles in 1923, with Poulson becoming a certified public accountant through correspondence classes and night school at Southwestern University.

In 1938, he was elected to the 56th District seat of the California assembly, then won a congressional seat four years later. After losing the seat in the 1944 election, he returned to the United States Congress following the 1946 elections, remaining there until his election as mayor of Los Angeles. Representing the city's 24th District during his years as a congressman, Poulson helped lead California in its fight against Arizona over Colorado River water. At the time of his departure from the United States Congress, he was the chairman of the Interior and Insular Affairs committee.

Poulson's victory in the Los Angeles mayor's race came after a contentious battle in which his opponent, incumbent mayor, Fletcher Bowron, claimed that the Los Angeles Times wanted to control city government, and by endorsing Poulson, would have a puppet in the mayor's office. Poulson, for his part, challenged Bowron's support for public housing, in particular a project in the area known as Chavez Ravine that later became the site of Dodger Stadium. Drawing on the anti-communist atmosphere of the time, Poulson promised to end support for "un-American" housing projects and to fire city employees who were Communists or who refused to answer questions about their political activities.

During his eight years as mayor, Los Angeles became the third largest city in the United States, with Poulson instrumental in leading the construction of the Los Angeles International Airport, expanding the Los Angeles Harbor and most notably, luring baseball's Brooklyn Dodgers westward. He helped integrate the city's Fire and Police Departments and initiated a garbage recycling program that proved to be a factor in his defeat in 1961.

Perhaps the most memorable image of his mayoral career came in September 1959, when he embarrassed Soviet premier Nikita Khrushchev during a public ceremony. The comments came after Khrushchev had constantly touted Russian superiority during his tour of the city by Poulson.

Citing Khrushchev's comment, "We will bury you," Poulson said, "You shall not bury us and we shall not bury you. We tell you in the friendliest terms possible we are planning no funerals, your or our own." Poulson received over 3,600 letters following the incident, many of them praising him for his comments.

He lost a reelection campaign in 1961 to Sam Yorty, partly due to having to explain the expenses incurred by the Dodgers' franchise shift. Efforts to blunt such criticism were limited due to a severe case of laryngitis from which he never recovered.

Following the defeat, Poulson briefly returned to accounting before moving to La Jolla, California in 1962.