Henry was the oldest son of Benjamin Seebohm (1798–1871) who was a wool merchant at Horton Grange, Bradford. The family had moved to England from Bad Pyrmont in Germany. Henry's mother Estther Wheeler (1798–1864) was a granddaughter of William Tuke. The Seebohms were active in the Society of Friends and Henry schooled within the community in York. He worked initially in a grocery as an assistant but moved to Sheffield where he became a steel manufacturer. He married Maria, daughter of George John Healey, a merchant in Manchester on 19 January 1859.
Henry became interested in natural history at school and continued to spend his spare time studying birds on his journeys. He travelled widely visiting Greece, Scandinavia, Turkey, and South Africa. His expeditions to the Yenisey tundra of Siberia were described in his two books, Siberia in Europe (1880) and Siberia in Asia (1882), which were combined in the posthumous publication The Birds of Siberia (1901). His expeditions included the lower Pechora River in 1875 along with John Alexander Harvie-Brown as well as a visit to Heligoland at the home of Heinrich Gätke. In 1877 he joined Joseph Wiggins to Siberia.
He was one of the first European ornithologists to accept the American trinomial system to classify sub-species.
Seebohm's other publications included A History of British Birds (1883), The Geographical Distribution of the family Charadriidae (1887), The Birds of the Japanese Empire (1890) and A Monograph of the Turdidae (1898).
- (1901) The birds of Siberia; a record of a naturalist's visits to the valleys of the Petchora and Yenesei. J. Murray. London.
- (1893) Geographical distribution of British birds
- (1890) The birds of the Japanese Empire. R. H. Porter, London.
- (1890) Classification of Birds. R. H. Porter, London.
- (1888) The geographical distribution of the family Charadriidae, or, The plovers, sandpipers, snipes, and their allies. H. Sotheran. London
- (1883) A history of British birds, with coloured illustrations of their eggs. R. H. Porter. London. Volume 1 Volume 2 Volume 3 Volume 4
- (1880) Siberia in Europe: a visit to the valley of the Petchora, in north-east Russia. J. Murray, London.
- (1880) Contributions to the ornithology of Siberia
- Seebohm, Henry; Sharpe, R. Bowdler (1896). Coloured figures of the eggs of British birds. Sheffield: Pawson and Brailsford. pp. v–xiv. The book was edited and published by RB Sharpe after Seebohm's death. Sharpe included a biography of Seebohm entitled Memoir at the beginning of the volume.