External-memory dictionaries are a fundamental data structure in file systems and databases. Versioned (or fully-persistent) dictionaries have an associated version tree where queries can be performed at any version, updates can be performed on leaf versions, and any version can be `cloned' by adding a child. Various query/update tradeoffs are known for unversioned dictionaries, many of them with matching upper and lower bounds. No fully-versioned external-memory dictionaries are known with optimal space/query/update tradeoffs. In particular, no versioned constructions are known that offer updates in $o(1)$ I/Os using O(N) space. We present the first cache-oblivious and cache-aware constructions that achieve a wide range of optimal points on this tradeoff.