Born into an artistic family, Gennari trained under both his father and uncle in Bologna, Italy. His early paintings particularly reflect the influence of his uncle, Baroque painter Guercino. In 1672 he travelled to Paris before crossing to England in 1674. He remained there for the next fourteen years, producing some 138 works and establishing himself as a notable painter to the Royal family. Although never officially granted a court appointment, his most significant commissions came from Charles II and his successor, James VII and II. Following the 1688 revolution, Gennari joined the exiled James in St Germaine-en-Laye, France, where he remained with the Jacobite court until 1692. He then returned to Bologna and in 1710 helped found the Accademia Clementina.