The Birth of Top 40
KOWH Omaha
In 1949, Todd Storz purchased a daytime station in Omaha, Nebraska. At the time, block programs and network entertainment shows were the norm for successful radio and music was a fill or part of a variety show.

The background is fuzzy, but the fact is that KOWH was the first station to base its programming exclusively on the top hits of the moment, with no other programming breaking up the constant rotation of the same few dozen songs.
Some say that Storz commissioned a study at a local university, others say that he saw an already finished study. But the study, whoever paid for it, said that people listened to the radio in their majority to hear music.

Storz' own anecdotal experience showed that people liked to hear the same "big songs" over and over. One version of that experience has him observing juke box play and observing that the same songs got most of the play.
Richard Fatherly, who passed in 2011, worked with Todd Storz and produced several narratives about the Storz stations. Mr. Fatherly sent me several documents to clarify points I missed. Read them:

Richard Fatherly's documents.

The audio segments are streamable by clicking any of these:

The Todd Storz Revolution - Radio's Happiest Broadcasters #1
The Todd Storz Revolution - Radio's Happiest Broadcasters #2
The Todd Storz Revolution - Radio's Happiest Broadcasters #3
The Todd Storz Revolution - Radio's Happiest Broadcasters #4
The 1958 DJ Convention
The Radio Revolution

To play:
Intenet Explorer: make sure that your system is set to play m3u files in your preferred audio player (usually Windows Media Player) via Control Panel -> Default Programs -> m3u and select your player if not set already.
Firefox: Tools -> Options -> Applications -> m3u and make sure your preferred audio player is selected.
So, some moment in about August of 1951 KOWH became the first all current hits station.

Rather than narrate the much discussed creative process behind KOWH, I thought it would be more interesting to show what happened after the format made it through its first ratings book. Here's one of the early ads... from February, 1953 just a month after the first full year of ratings was released.

Click for a larger PDF of the ad.
A series of similarly themed ads followed.  Here is another from 1952:
Later in 1953, the theme changed but the numbers held strong.
By 1954, WTIX in New Orleans and WHB in Kansas City had been added but the theme was the same.
There are many more ads and they later feature additional stations like WQAM and WDGY and KOMA that were added to the group. To demonstrate the search feature of this website, here is a link to a search that will give you several hundred KOWH references. Click on the picture of Mr. Storz to see them.
Or, if you want to search for the other stations, go to the Broadcasting Magazine resource page and enter search terms like "Storz" or "WQAM" to read further about what started the rebirth of radio. I'd suggest limiting the search to the 50's to reduce the quantity of links you will generate.