On screen, the answer is, at present, no. He has used the phrase "The people I love" ("A Good Man Goes to War"), but the character himself has never been heard to say "I love you." Instead, he has used other expressions. Steven Moffat has stated, for example, that in his opinion the Doctor's statement "Do you think I care so little for you that betraying me would make a difference?" in his script for "Dark Water" was the Doctor's way of saying "I love you" to Clara Oswald. Other acknowledged expressions include "I had a duty of care" in "Hell Bent" (again addressed to Clara) and "Hello, sweetie" in "The Husbands of River Song" addressed to River Song.
In "Journey's End", the Meta-Crisis (cloned) Tenth Doctor is seen whispering something to Rose Tyler that results in her kissing him romantically, which may have been "I love you" but as this is not heard on screen this cannot be definitively confirmed.
Several characters have said "I love you" to the Doctor, however. The (very) short list includes Rose Tyler ("Doomsday"), The TARDIS matrix inhabiting Idris' body ("The Doctor's Wife"), Clara Oswald ("Mummy on the Orient Express": confirmed by the actress in multiple convention panels), and River Song (not the exact phrase, but close enough in "The Husbands of River Song" and she also referred to the Doctor as "My Love".)