In order for a character to be defined as a tragic hero, he must be noble in character. Jay Gatsby demonstrates this in his devotion to Daisy Buchanan, whom he has been preparing for a re-encounter with for the past 5 years. When he finally finds himself in her presence again, "...there were twinkle-bells of sunshine in the room, he smiled like a weather man, like an ecstatic patron of recurrent light..." He talks with Daisy, and even after 5 whole years of building her up in his mind, he is still very much in love with her. "...[After speaking with her,] there was a change in Gatsby that was simply confounding. He literally glowed; without a word or a gesture of exultation a new well-being radiated from him and filled the room." He loves her, everything he does is for her, and there is no characteristic more noble than true love and devotion.
The very denotation of a tragic hero is a noble person with a tragic flaw which helps to bring about his downfall, and which may cause the hero to make poor decisions. Mr. Gatsby's character flaw is his enduring dream of finding Daisy, the woman he met and fell in love with before he was sent to fight in World War I, and reuniting with her. When they met, he was a poor nobody and she was a member of the old-money elite, a match that they both knew could not possibly work. So, even though he knew she was married, when Jay came back from the war, he devoted his life to reinventing himself to make himself good enough