Balck was born in Karlskrona, Sweden, and was a sailor in his youth. In 1861, he joined the Swedish War Academy at Karlberg in Stockholm as an officer cadet of the Swedish Navy. After a while, he switched track to become a cadet for the Swedish Army, and was active in fencing and gymnastics. He stayed on as assistant gymnastics instructor at Karlberg for a while, and in 1866 was commissioned as a second lieutenant in the Närke regiment. He was promoted to lieutenant in 1875, in the same regiment, and to captain in 1884.
However, Balck's military career came to be devoted almost entirely to gymnastics and sports. He was assistant instructor at Karlberg from 1868 to 1870, then gymnastics teacher at the Swedish cavalry riding school at Strömsholm, 1870-1872. He became an instructor of military gymnastics and fencing at the Swedish Central Institute of Gymnastics in 1885, was chief instructor in the same subject, 1887-1909, and the Institute's director 1907-1909. He was promoted to major in the Swedish Army in 1894, to lieutenant colonel in 1900, and to colonel in 1904. In 1909 he transferred to the reserve list and in 1914 received an honorary promotion to major general.
Directly after completing his officer's training, Black studied the pedagogical, military and medical course at the Swedish Central Institute of Gymnastics 1866-1868, and stayed on as assistant teacher at the Institute 1868-1870, while also being an assistant teacher at Karlberg. From 1872, his main activities - both in military and civilian gymnastics and sports - had the Institute as a base.
As a young officer and gymnastics teacher, Balck was of the impression that voluntary gymnastics and sports activities in Sweden, i.e., outside the army and the schools, were undeveloped in comparison to the contemporary situation in many other countries. Determined to change this, from the 1870s he participated in the formation of several sporting clubs and organisations, and the founding of several related journals. During this time, Swedish organised sports took shape, and Balck became one of its leading figures.
Balck also became involved in the emerging international sports movement at the end of the 19th century. In 1894 he became one of the original members of International Olympic Committee (IOC), and was one of two vice presidents of the Swedish Olympic Committee from 1913 to his death in 1928. He was also one of the leading figures behind the Nordic Games which were arranged from 1901.