Peterson was born in Bergen, Norway. In Norway, he became a member of the Religious Society of Friends and emigrated to the United States in 1837. In 1842, while living in La Salle County, Illinois, he became a member of the LDS Church. After joining the church, he became a missionary to Norwegians living in Wisconsin.
From 1853 to 1855, Peterson was a missionary in the Scandinavian Mission, where he preached in Norway and became the president of the Christiana Conference of the church. Later, from 1871 to 1873, Peterson returned to the Scandinavian Mission as the Mission president, where he guided the missionary work in Norway, Denmark, and Sweden.
In 1867, Peterson was asked to move to Ephraim, Utah to be a bishop of the church there. Peterson was instrumental in assisting the Latter-day Saints make peace with the Native Americans in Sanpete County. The Canute Peterson House, a house he built in Ephraim, is listed in the U.S. National Register of Historic Places.
On 1882-10-14, Peterson became a member of the Council of Fifty. When Peterson died in Ephraim, Utah, he was serving as the president of the Sanpete Stake, a position he held since 1877. Peterson was also ordained to the office of patriarch. Peterson is considered to be one of the founders of Snow Academy, know today as Snow College.