Anaxicrates was active in the early Hellenistic period during the 4th–3rd centuries BCE. The epithet "Historicus" distinguishes him from other figures of the same name. His likely subject matter was the transition from the Classical to the Hellenistic age, including the wars of Alexander the Great's successors.

His only known work is On Cities, which survives only in fragments. These are preserved primarily through citations in later authors like Athenaeus.

Anaxicrates is a minor fragmentary historian. His On Cities was a geographical or historical survey detailing the foundations and customs of various cities. The extant fragments, often cited for details on local luxuries or customs, illustrate how such lost local histories served as sources for later compilers, preserving localized Hellenistic knowledge.