Ostergaard immigrated to the United States where he worked at Danish language Folk high schools. He taught at the Elk Horn Højskolein in Elk Horn, Iowa from its beginning in 1878. He also helped establish the Ashland Folk School at Grant, Michigan in 1882.
In 1885 he returned to Denmark, where he founded a Folk high school in Støvring (now Rebild municipality in Region Nordjylland). In 1892, Ostergaard returned to the United State. He was ordained a Lutheran pastor in 1893. He served the ministry of the United Evangelical Lutheran Church. He ministered to a number of congregations before retiring in 1916 at Tyler, Minnesota. Ostergaard devoted the remainder of his life to writing songs, poetry and fiction. His writings were all in the Danish language.
Ostergaard wrote a number of novels depicting the life among Danish-American immigrants. His novels provided accounts of the immigrants struggling to create communities on the prairies, mostly Nebraska. Several trace members of a family from their arrival in the early 1870s to their participation in settling Nebraska.
Ostergaard also wrote many songs and hymns an anthology of which was published in 1912. Most notably, Ostergaard wrote the hymn Den Sag er aldrig i Verden tabt. Translated into English by Jens Christian Aaberg as That Cause Can Never Be Lost Nor Stayed, it was published in Hymns and Hymnwriters of Denmark during 1945.
- A Merchant's House (1909)
- Songs of the Prairie (1912)
- Dalboerne (1913)
- The Scandinavian Immigrant Writer in America(by Dorothy Burton Skardal. Norwegian-American Historical Association. Volume 21: Page 14) 
- The Danish Folk High School and Its Reception in the United States: 1870s-1930s (Harold W. Stubblefield and Patrick Keane. Jossey-Bass Publishers. 1994)
- Kristian Ostergaard 1855-1931 (Cyber Hymnal)
- Kristian Ostergaard's A Merchant's House (John Mark Nielsen, University of Nebraska-Lincoln) 
- That Cause Can Never Be Lost Nor Stayed (Cyber Hymnal)
- Hymns and Hymnwriters of Denmark (Christian Classics Ethereal Library) 
- The Cross Church at Danebod (Danebod Lutheran Church)
- Mortensen, E. Schools for life: The Grundtvigianfolk schools in America (Askov, MN: American Publishing Co. 1977)
- Larson, D. C. The movement to preserve Danish culture in North America (Pittsburgh. PA: University Center for International Studies, University of Pittsburgh. 1980)