There were not "conversion" at all, but a progressive involvment with logic and language.
For historical evidence, see e.g. Letter to B.Russell [Nov.1913], with refernce to Bedeutung [reference] (a key-term of Frege's Philosophy of language) in relation to facts and proposition.
For W's philosophy of language in the Tractatus (1921), you can see Wittgenstein's Logical Atomism.
For early philosopical interests of Wittgenstein, we can see : Notes on Logic (1913); for details, see Michael Potter, Wittgenstein's Notes on Logic, a book fully dedicated to the first (unpublished) W's work, deeply involved with Russell's and Frege's philosophies about logic and language.