The phrase "Elementary, my dear Watson" with the same arrangement of the words, has never been expressed even once in any Sherlock Holmes story.
The closest you can get, however, seems to be in the story titled "The Adventure of the Crooked Man":
“I have the advantage of knowing your habits, my dear Watson,” said he. “When your round is a short one you walk, and when it is a long one you use a hansom. As I perceive that your boots, although used, are by no means dirty, I cannot doubt that you are at present busy enough to justify the hansom.”
“Excellent!” I cried.
“Elementary,” said he. “It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbour, because the latter has missed the one little point which is the basis of the deduction.
And in "The Hound of the Baskervilles":1
“Interesting, though elementary,” said he, as he returned to his favourite corner of the settee. “There are certainly one or two indications upon the stick. It gives us the basis for several deductions.”
The first, or what seems to be the first occurrence of the exact phrase, appears to have been in the newspaper "Richmond Times Dispatch" in 1909:2
The possibility of signaling to the planet Mars is merely a question of elementary mathematics.… It is such a simple little problem that any one should be able to take a pad and pencil and work it out in ten minutes. “Elementary, my dear Watson,” as Sherlock Holmes was wont to say. “Elementary.”
A very close phrase was said even earlier, by the "Northampton Mercury" in 1901, however, it was actually in a parody of Sherlock Holmes, with the characters named "Shylock Combs" and "Poston":3
One winter’s morning, a few years after my marriage, I was lying by my hearth, smoking a red herring, and nodding over the Encyclopedia Britannica, for my day’s work had been a hard one. Since first meeting Shylock Combs my practice as a doctor had, as a matter of course, rapidly declined. My presentation clock had chimed 4.47 a.m., and I was in the act of blowing out the gas when I heard the clang of my front door speaking tube. Thinking it must be the milkman I went into the hall, opened the door, and, to my astonishment, Shylock Combs stood upon my step. “Ah, Potson,” he said; “I hoped I should not be too early to catch you. I perceive the wind has changed round to N.N.E. by S.W. again.” I was astounded, as he had not had time to observe the thermometer in my bedroom. He noticed my amazement and smiled that wonderful smile of his. “Elementary, my dear Potson,” he said; “I observed the left-hand side of your moustache inclined about 47 5/8 degrees towards the west, and coming as I did from Butcher-street I at once deduced from which quarter the wind was blowing.”3
(all emphasis is mine)
1 August 27 2013, Today I Found Out
2 August 24 1909, The Times Dispatch, “Signaling to Mars: An Elementary Problem, Says Professor Pickering, of Harvard”, (Acknowledgment to Rochester Post-Express), Quote Page 6, Column 7, Richmond, Virginia. (Chronicling America)
3 November 15 1901, The Northampton Mercury, Sherlock Holmes’s Latest!, Quote Page 6, Column 3, Northamptonshire, England. (British Newspaper Archive)