The son of a rural clergyman, Kellgren became a lecturer in poetry and classical literature. A talented and ambitious young man, he soon found his way to the court of Gustav III. For some time he acted as private secretary to the king, who appointed him one of the first members of the Swedish Academy when it was founded in 1786. Kellgren's earliest works (erotic poems) appeared in 1773, but he won fame with the satiric poem Mina löjen (1778; “My Laughter”). In the 1780s he wrote a number of verse dramas on themes suggested by Gustav. This collaboration culminated in Gustaf Wasa (1786), a successful patriotic opera. The following year he wrote what is considered his greatest poem, Den Nya Skapelsen, eller inbillningensvärld (1790; “The New Creation, or the World of the Imagination”), in which he exalts the cosmic power of the imagination while describing a rich experience of romantic love.

From 1778 until the time of his death, Kellgren was associated with the influential literary journal Stockholmsposten, which he edited in the years 1780–84 and 1788–95. A sensuous poet and a radical defender of the Enlightenment from Voltaire to the French Revolution, Kellgren used his literary and intellectual skills to attack superstition and criticize a broad array of social vices. He was also the first to fully recognize the poetic and musical genius of Carl Michael Bellman (Bellman, Carl Michael).