。
He woke up to find himself famous.
Literal
Eye [subject-が] wake-up-[and-see-てみる][when-と] famous had-become.
~てみる ('try X-ing / do X and see what happens') is layered onto 覚める — 'upon waking and seeing what was the case.' The auxiliary adds a sense of discovery: you perform the action and the result then becomes apparent. Paired with the past resultative になっていた ('had become'), the whole frame captures 'upon waking, it turned out that…' — a structural echo of the Byron story about waking up famous.