Kauffman was born at Chur in Graubünden, Switzerland. Her family moved to Morbegno in 1742, then Como in Lombardy in 1752 at that time under Austrian rule. In 1757 she accompanied her father to Schwarzenberg in Vorarlberg/Austria where her father was working for the local bishop. Her father, Joseph Johann Kauffmann, was a relatively poor man but a skilled Austrian muralist and painter, who was often traveling for his work. He trained Angelica and she worked as his assistant, moving through Switzerland, Austria, and Italy. Angelica, a child prodigy, rapidly acquired several languages from her mother, Cleophea Lutz, including German, Italian, French and English. She also showed talent as a musician and was forced to choose between opera and art. She quickly chose art as a Catholic priest told Kauffman that the opera was a dangerous place filled with "seedy people." By her twelfth year she had become known as a painter, with bishops and nobles being her sitters.
In 1754, her mother died and her father decided to move to Milan. Later visits to Italy of long duration followed. She became a member of the Accademia di Belle Arti di Firenze in 1762. In 1763 she visited Rome, returning again in 1764. From Rome she passed to Bologna and Venice, everywhere feted for her talents and charm. Writing from Rome in August 1764 to his friend Franke, Winckelmann refers to her popularity; she was then painting his picture, a half-length; of which she also made an etching. She spoke Italian as well as German, he says, and expressed herself with facility in French and English - one result of the last-named accomplishment being that she became a popular portraitist for British visitors to Rome. "She may be styled beautiful," he adds, "and in singing may vie with our best virtuosi". In 1765, her work appeared in England in an exhibition of the Free Society of Artists. She moved to England shortly after and established herself as a leading artist.