Born in Antwerp as the son of painter Elias Voet, Jacob left for Rome around 1663 and became part of the Bentvueghels, a group of Dutch and Flemish artists. He gained popularity for his portrait work, receiving commissions from the Papal court and notable families like the Colonna and Odescalchi. Notably, he painted portraits for Christina, Queen of Sweden, and created a celebrated series of 37 portraits of Roman society's young women for Cardinal Chigi.
His provocative depictions of women led to a ban from Rome by Pope Innocent XI, after which he worked in Milan, Florence for the Medici, and Turin before returning to Antwerp in 1684. He later moved to Paris, where he became a prominent court painter, capturing the likenesses of political and military figures until his death in 1689.