Henri Kling was born in Paris on 15 February 1842. His father, Ludwig Christoph Kling, came from Germany; his mother, Claudette, née Rémy, was French.
At the age of two, Kling moved with his parents from Paris to his father's home town and grew up in Karlsruhe. His mother died soon afterwards, and his father remarried. Kling studied horn in Karlsruhe with Jacob Dorn. At the age of 20 he was engaged as a horn player in the orchestra of the “Grande Théâtre”, the Geneva opera house of the time, and also played in the Pepin Orchestra. In 1865 he published a highly regarded horn method. In 1866 he became teacher of music theory, solfège and horn at the Conservatoire de musique de Genève, a position he held until his death.
Kling's musical interests were wide-ranging. He worked as organist at the church in Cologny and at the church of Saint-Germain in Geneva, conducted the casino orchestras in Geneva and in Evian-les-Bains (France), and directed the “Corps de Musique de Landwehr”, the official wind band of the Republic and Canton of Geneva (Switzerland). He also taught music and singing at a girls' secondary school in Geneva.
As a composer he wrote works for orchestra, wind band, music theatre, church music, vocal music, chamber music and pedagogical works. Kling arranged Wolfgang Amadeus Mozart's horn concertos for the modern orchestra and wrote the cadenzas for them. He also arranged Carl Maria von Weber's Concertino for horn and orchestra, op. 45, as well as Mozart's Clarinet Concerto in A major, K. 622, and Bassoon Concerto in B-flat major, K. 191.