In 1759, he joined the company of Giuseppe Forti, which performed in Venice at the Teatro San Moisè, with the stage name Galeotti.

In 1769–1770 they were in London at the Haymarket Opera where Galeotti choreographed dances for Christoph Willibald Gluck's Orfeo ed Euridice.

In 1775, Galeotti was called to Copenhagen to assume the directorship of the Royal Danish Ballet, replacing another Italian, Antonio Sacco.

He created the first ballet with a Nordic subject (Lagertha, 1801, based on the legendary Viking shieldmaiden), as well as the first choreographies inspired by William Shakespeare (Romeo and Juliet, 1811, and Macbeth, 1816), with music written by Claus Schall.

Galeotti's most lasting success, and the only work by him still commonly performed today, is Amors og Balletmesterens Luner (The Whims of Cupid and the Ballet Master, 1786),[1] which is the oldest European ballet still danced to its original choreography and music (by Jens Lolle [da]);[2] it has been staged more than 500 times.