Yes he did, BP, but Conan Doyle never wrote it as such. I'm thinking that a radio series some decades ago (the 30s?) planted the catchy version that we mistakenly attribute to him today.
Consulting my box set "The Annotated Sherlock Holmes" by William S. Baring-Gould, the Actor William Gillette uttered the line "Oh, this is elementary, my dear Watson in the 1899 play "Sherlock Holmes" in which he wrote and starred in.
In the 1929 movie "The Return of Sherlock Holmes" the line "Elementary, my dear Watson, elementary" was said. Of course there are the few times a variation of these lines appeared in the many Basil Rathbone film interpretations.
So yes the "Elementary, my dear Watson" did not appear in the canon. Neither did Holmes wear the famous "Deerstalker" even though Sidney Paget did illustrate Holmes wearing one in "Silver Blaze", Watson only describes it as his (Sherlock's) "...ear-flapped travelling-cap...". And so the myths continue.
Thanks to Google search, people can appear to be smarter than they really are.