I Could Have Danced All Night was composed by Frederick Loewe, with lyrics by Alan Jay Lerner. It's from the 1956 musical My Fair Lady, which is of course an adaptation of George Bernard Shaw's 1913 play Pygmalion... or, more accurately, it's adapted from the 1938 film adaptation of Shaw's play. The song occurs in Act I; after many frustrating efforts, Eliza has finally gotten her diction lesson right, resulting in the triumphant song & dance The Rain In Spain. Afterwards, Henry Higgins' housekeeper and maids urge Eliza to go to bed- it's the early hours of the morning- but she is too exhilarated and happy to sleep, resulting in the song I Could Have Danced All Night.
In the original musical, Eliza was played by Julie Andrews but for the 1964 film version, the part was given by Audrey Hepburn. This was before Mary Poppins and The Sound of Music, and so Julie Andrews was passed over for a well known movie star. In retrospect, this was of course the wrong decision especially since Hepburn, though a fine actress, didn't have the vocal skills to pull off the songs... her singing voice had to be dubbed by Marnie Nixon, of whom I've written before.
I couldn't find a video of the SATB choral arrangement- by William Stickles- that we're working on, but here is a recording of Julie Andrews singing I Could Have Danced All Night: