In Greek mythology, Hesiod composed Works and Days, the poem containing Pandora’s story. Hesiod was an ancient Greek poet generally dated to the late eighth or early seventh century BCE.
Works and Days is a didactic poem concerned with farming, justice, labor, and the proper ordering of human life. Its account of Pandora appears within a broader explanation of why toil and suffering exist. The poem is therefore more than a standalone adventure about opening a container.
Hesiod also wrote Theogony, a major poem about the origins and genealogies of the gods. The two works are important early sources for Greek mythology, but they do not treat every myth in the same way. The Pandora episode associated with the opened jar is especially connected with Works and Days.
Homer is often named alongside Hesiod as a foundational Greek poet, but Homer did not compose the Pandora episode in Works and Days. That distinction makes Hesiod the specific answer here.