Kock was born in a merchant family in Trelleborg, but lost both parents at an early age and was raised in the home of the Tegnér family in the university town of Lund, where he became friends with Esaias Tegnér Jr.

He studied in Lund and Strassburg, finished both his licentiate and doctorate degrees in 1879 and became a university docent of Scandinavian languages the same year.

He resigned from the chair in 1893, possibly because of his bad eyesight, and spent the next several years without an academic position.

He accepted the professorship of Scandinavian languages at Lund when it was offered to him in 1907 and retained it until his retirement in 1916.

[1] Kock was a prolific contributor to the journal Arkiv för nordisk filologi already from its start in 1883, and served as its editor-in-chief from 1888 until 1928.