What are some songs that originated in Broadway musicals and became hits on the radio? Define “hits” as you will - Top 40, Top 100, etc. I can think of a few.
From Evita (the 1996 theatrical version) we have Madonna’s Don’t Cry For Me Argentina, which I’m pretty sure was a Top 10, if not Top 40, hit c. 1996.
And from Chess, we have possibly the most niche and esoteric song to ever be a radio hit, One Night In Bangkok
As an Honorable Mention, I’ll throw out It’s a Hard Knock Life, from Annie (the 1982 film), which gets sampled pretty heavily in Jay-Z’s song of the same name.
A nitpick here: those two songs, as well as the other hit, “Hopelessly Devoted to You,” were specifically written for the film version, and weren’t in the Broadway production.
Not exactly the way described in the OP - Puttin’ on the Ritz first appeared in a film of the same name in 1930, which was a story about a Broadway musical. Later it became a hit in 1982 in a rendition by Taco, then in 2007 was featured in the Broadway version of Young Frankenstein.
Going back a ways (and to one of my favorite musicals), “Till There Was You,” from The Music Man (1957), reached #30 on the Billboard chart and #14 on the Cashbox chart.
And later was covered by the Beatles, though it never was a single and thus no hit. As a kid, I had it on a compilation named “And Now: The Beatles”, and I thought it was the lamest song they ever had done, grown-up/parents music to my ears.
If we want to be really pedantic — and I’m sure nobody here wants that, right? — we should distinguish between a recording of a song from a cast album, where the actors in a stage production record their songs in a studio to be released in connection with (or shortly after) the opening of the live performance run, and the unusual thing that “One Night in Bangkok” is.
See, as they were conceptualizing the show, they knew it was going to be expensive to produce on stage. So they recruited some performers and made a concept album out of the songs they had at the time, in order to drum up interest and publicity, and attract investment. The song that became the radio hit is from this concept album.
So the pedantic distinction is this: “One Night in Bangkok” is, indeed, a song from the musical Chess. But at the time it exploded in popularity, it was not yet, technically, a musical, because it hadn’t been mounted yet. Indeed, it wasn’t even done. After the success of the album (and the song), they did further work, writing the book and some new music, and changing a few of the songs, and then they finally produced the show in London, with some (but not all) of the same performers they used on the concept album. (And the additional changes they made between London and the New York premiere are a whole nother post by themselves.)
So, yes, “One Night in Bangkok” is a song from the musical Chess, and it was a radio hit. But… when it was a radio hit, is it better described as a song from a musical, or a song from a proposed musical, still in progress?
Looks like I’ll Never Fall In Love Again made it to Broadway thanks to “Promises, Promises” in ‘68, before Dionne Warwick’s ‘69 recording then hit #6 on the charts.
“Try to Remember” is from The Fantasticks (1960) and was originally sung by Jerry Orbach (yes, the same guy from Law & Order). The song has charted in the U.S. several times, with covers by Ed Ames, Roger Williams, The Brothers Four, and Gladys Knight & the Pips (as a medley with The Way We Were).
Technically the Beatles version was NOT a cover. McCartney learned it from a Peggy Lee album. It wasn’t until many years later that he figured out it was originally from The Music Man.