Eielsen was born on the farm of Sunve in Voss, Norway and brought up in the religious tradition of Hans Nielsen Hauge. After his own religious awakening at the age of 25, he moved to Bergen, where he served as an apprentice as a carpenter and blacksmith and also enlisted in the army. He acted as a spiritual leader among his fellow soldiers, and in 1832, he accepted his first mission as a lay preacher.
He traveled for several years extensively throughout Norway, and also preached in Denmark, where he was arrested and briefly imprisoned. Eielsen emigrated to the United States where he stayed for some time at the earliest settlements there. On October 3rd 1843, he was formally ordained as a Lutheran minister by Dr. F.A. Hoffmann, and in 1846 he founded the Evangelical Lutheran Church in America (Eielsen Synod)
He returned to Norway in 1861 through 1862, but returned to the United States where he became an itinerant pastor until he died in Chicago.