The song was one of several introduced in the film The Fleet's In (1942). It was sung in the film by Dorothy Lamour (with harmony by Bob Eberly and Helen O'Connell and featuring the Jimmy Dorsey Orchestra) and is one of the songs most associated with the singer/actress. Schertzinger, who co-wrote all the film's songs with Mercer, was also the director of the movie.
According to the TCM documentary Johnny Mercer: The Dream's On Me, Mercer wrote the song for Judy Garland, to express his strong infatuation with her. He gave it to her the day after she married David Rose.
Was it in Tahiti? Were we on the Nile? Long ago, say an hour or so, I recall that I saw you smile.
And, I remember you. You're the one who made my dreams come true, A few kisses ago.
I remember you. You're the one who said "I love you, too. I do. Didn't you know?"
I remember, too, A distant bell and the stars that fell like rain Out of the blue.
Well, when my life is through And the angels ask me to recall the thrill of them all Then I shall tell them, "I remember you."