Boquist was born and raised on a dairy farm in Tillamook, Oregon. He attained the rank of Eagle Scout in the Boy Scouts of America, graduated from Tillamook High School, and enlisted in the United States Army in 1975. He earned a Bachelor of Science degree from Western Oregon State College (now Western Oregon University) and an MBA from Oregon State University.
Boquist is a former career special forces lieutenant colonel who served in branches of the United States Army. He is a director with International Charter Incorporated, an international services company that specializes in a variety of support operations for private organizations and the United States government. ICI has worked in Africa, Asia, the Middle East, and South America. Additionally, ICI was involved in pre-deployment training of armed services members during OEF and OIF from 2006 to 2012. Boquist is involved with several other business entities primarily in the agriculture and forestry industry. He served as Deputy Commander and Chief of Staff of the Joint Combined Special Operations Task Force in Iraq in 2003–2004, receiving the Bronze Star Medal and recommendation for promotion for his service.
Boquist ran for the U.S. Senate in 1996, taking less than 1% in the Republican primary. In 2000, he was the Republican nominee for the United States House of Representatives in Oregon's 5th congressional district, but lost with 43% of the vote to incumbent Darlene Hooley. Boquist challenged Darlene Hooley in the 2002 General Election, losing as second time with 45% of the vote.
In 2004, Boquist decided against a run for Hooley's seat, but when Oregon state representative Lane Shetterly resigned to run the Oregon Department of Land Conservation and Development commission, Boquist chose instead to run for Shetterly's seat in Oregon House District 23. Though Jim Thompson was named by Oregon Republicans to complete Shetterly's term, Boquist defeated him in the Republican primary and went on to win the general election with 61% (17,390) of the vote. Boquist was re-elected to the Oregon House of Representatives in 2006 with 58% (13,422) of the vote.
In the 2008 Republican primary, Boquist announced that he was leaving the Oregon House to seek election to the state Senate. He was unopposed for his party's nomination to represent Oregon Senate District 12 and faced Democrat Kevin Nortness in the general election. He won the general election 61% to 39% garnering 33,264 votes. (Jim Thompson, whom Boquist defeated for the state House in 2004, won the election with 15,878 votes to succeed Boquist in the House.) Boquist was re-elected the Oregon State Senate in 2012 with 60% of the vote, garnering 34,038 votes.
Boquist serves as the Chairman of the Veterans and Emergency Preparedness Committee in the Oregon State Senate. He was closely involved in the 2013 Regular Session, and following Special Session, with the passage of the small business tax cut to incentivize job grow in rural Oregon. He was appointed to serve on the oversight committee for the start up of the Cover Oregon insurance exchange during which time he constantly sought expanded committee authority to place witnesses under oath and subpoena testimony, both of which were never granted to the now defunct committee.
Boquist and his wife Peggy have six grown children and live near Dallas, Oregon. Their son Sethan Charles Sprague committed suicide in 2016 at age 31, likely related to trauma from his time in the Navy.