Lye's New Spelling Book (1677) was the first to list "zee" as a correct pronunciation, and it was pretty much firmed up by Webster, who, like grammarians all over the former Empire, wanted to put the kibosh on all this "izzard" nonsense, and decreed "it is pronounced zee" (1827).
This so-called "Sesame Street Phenomenon" is noted in almost all other English-speaking countries, and was addressed by J.K. Chambers in a study of kids in Ontario, in which he noted a lessening of the taboo on "zee" in the Canadian schools. Even in England itself, elementary teachers are complaining that they have to re-teach the pronunciation of the letter when 5 and 6 year olds come to school, and when they sing the song, they typically do so with the American pronunciation.
Now you know about zed and zee. Next time won't you sing with me? 
