He attended Brigham Young University and later served as a missionary for The Church of Jesus Christ of Latter-day Saints in Guayaquil, Ecuador.

He played Sir Sagramore in Camelot at Lincoln Center and Chris in the second national tour of Miss Saigon.

[8] Audra McDonald and Swenson reprised their roles in a two-week fundraising production of 110 in the Shade at the Hale Center Theater in Orem, Utah.

In 2010 in Toronto, Canada, Swenson played the lead role of "Tick"/"Mitzi" in the pre-Broadway North American company of Priscilla: Queen of the Desert.

[10] In October 2013, Swenson was cast as Inspector Javert in the 2014 Broadway revival of Les Misérables, which opened in March 2014 at New York's Imperial Theatre, where the musical had previously run for 13 years.

The show moved to Broadway later in 2022 officially opening on December 4, at the Broadhurst Theatre in New York City.

In October 2020, Swenson joined other Broadway stars in a virtual letter-writing event hosted by nonpartisan voter advocacy group VoteRiders.