Born in Utah, Swenson was the daughter of Swedish immigrants, and in her large Mormon household, English was a second language. Swenson earned her degree at Utah State University, where her father taught mechanical engineering. A writer from an early age, Swenson moved to New York City in 1935 to pursue her writing career, holding various jobs before becoming the editor of New Directions Press in 1959. Her first volume of poems, Another Animal, was published in 1954.

Swenson was a very prolific poet, publishing several volumes of poetry throughout her lifetime. She also wrote three collections of poetry for children, one play, and has translated works by Tomas Tranströmer.

Her poetry is known for its keen observation, playfulness, and constant questioning of the world surrounding her.

–Christie Finn