Eddie was the first single to be released from the Rocky Horror Show. It was released as a "B" side on the Kimi and Ritz single "Merry Christmas Baby"/"Eddie" in December 1973.
The Kimi and Ritz version is slower than most other versions and is sung by Kimi Wong, who at the time was Richard ("Ritz") O'Brien's wife.
For more on Kimi and Ritz, check out http://en.wikipedia.org/wiki/Kimi_and_Ritz .
"Eddie" does not appear on the original London soundtrack, and was only added to the play after it moved from the Theatre Upstairs to the Classic Cinema.
For more versions of the song than you can shake a stick at, check out http://www.rockymusic.org/tags/Eddie%27s+Teddy.php - includes several cast renditions, as well as fragmentary renditions by Richard O'Brien himself and Jonathan Adams.