"Na Na Hey Hey Kiss Him Goodbye" was written and recorded by Paul Leka, Gary DeCarlo and Dale Frashuer, attributed to a then-fictitious band they named "Steam".  It was released under the Mercury Records subsidiary label Fontana and became a number one pop single in late 1969, and remained on the charts in early 1970.

DeCarlo, Frashuer and Leka had been in a band together called the Chateaus in the early '60s.  One of the unfinished songs they wrote as the Chateaus was a tune called "Kiss Him Goodbye," which they worked on in 1961.

In 1968, Leka was writing with DeCarlo, who was using the stage name Garrett Scott.  Working for Mercury Records, they set to work writing singles for "Garrett Scott," recording songs which Leka produced.  

As they assembled a group of songs, they needed B sides to the singles. B-sides in the '60s were often ad-hoc affairs designed to be clearly inferior to the A-side so that disc jockeys wouldn't flip the record.

Leka and DeCarlo were joined by their old bandmate Dale Frashuer, who suggested they use their 1961 song "Kiss Him Goodbye."  That song didn't have a chorus, so Leka wrote one, lazily using "na na"s instead of actual words.

The three musicians who recorded this had that in mind for this song and kept it simple: there is no bass or guitar on the track, and the repeating drum loop was lifted from a song written by Neil Sedaka.  Na Na Hey Hey was built in layers, with just the drum track, piano, organ and a board DeCarlo played as percussion to accompany the vocals.

When Bob Reno, the A&R man at Mercury, heard the song, he loved it and didn't want to waste it as a B-side. He needed singles so the song was released and credited to the group Steam (named because after the session to record it the guys were crossing 7th Ave and a subway train went beneath the roadway, shooting steam up from a manhole). When this song became a hit, an entire album was commissioned, and a group created for it.  The song's singer and co-writer, Gary DeCarlo, sang backup on the other tracks but refused to sing lead on them, since he was not invited to tour with the band and hated the idea of other guys taking credit for his work

The Chicago White Sox organist, Nancy Faust, first started playing it in 1977. When the other team’s pitcher was removed, Faust played the song; when the White Sox won, she’d play the song.  Played on an organ, the sustained notes somehow making the song’s taunting quality even more pronounced, “Na Na Hey Hey” didn’t just become synonymous with the White Sox —  it became a trademark for the organist.

Various Sources