"Bibbidi-Bobbidi-Boo" (also called "The Magic Song") is a novelty song, written in 1948 by Al Hoffman, Mack David, and Jerry Livingston. It was introduced in the movie Cinderella, in 1950.
A recording by Perry Como and The Fontane Sisters was the most popular. It was recorded on November 7, 1949. The flip side was (another one from Cinderella) "A Dream Is a Wish Your Heart Makes." The recording reached #14 on the Billboard chart.
Another recording, by Jo Stafford and Gordon MacRae, was released by Capitol Records (although there's just something about Jo Stafford's voice I don't like, listen to that version here). The record first reached the Billboard magazine charts on December 16, 1949 and lasted 7 weeks on the chart, peaking at #19.
But obviously the best version of the song is in its original inception, in the Disney classic, Cinderella, with Verna Felton as the Fairy Godmother: