Born in Aalborg, Denmark, on 1 November 1847, Jacob Johnson immigrated to the United States in 1854 with his mother after his father died. He lived in Ogden until 1863 when he moved to Sacramento, California. In 1869 he moved to Carson City, Nevada, and then the White Pine Mining District, where he studied law. In 1872 he moved to Spring City, Sanpete County, Utah, where he began his law practice and where he also engaged in agricultural pursuits.

Johnson served as United States district attorney from 1880 to 1881 and as a United States Commissioner for Utah from 1881 to 1893. He was also a probate judge of Sanpete County from 1888 to 1890, prosecuting attorney of Sanpete County from 1892 to 1894, and judge of the Utah Seventh Judicial District from 1896 to 1905. As district judge, he was responsible for most of southeastern Utah, including Sanpete, Carbon, Emery, Grand, and San Juan counties. Elected as a Republican, he served in the United States House of Representatives from 1913 to 1915. He failed to secure his party's renomination in 1914.

After his congressional term, Johnson practiced law in Salt Lake City. He had married Margaret Anderson in October 1873, and the couple were the parents of two sons. After her death on 15 December 1885, Johnson married Matilda Justesen of Spring City, by whom he fathered two sons and four daughters.

Jacob Johnson died on 15 August 1925 and was buried in Salt Lake City on 17 August following funeral services in the Masonic Temple. The Jacob Johnson house and barn still stand in Spring City and have been listed in the National Register of Historic Places for their historic and architectural significance.