Sources familiar with the deal told both outlets it includes the singer's recorded music catalog as well as his body of work as a songwriter -- including classic hits such as "Born to Run," "Blinded by the Light" and "Born in the U.S.A."
No public announcement has been made. Sony Music didn't immediately respond to requests for comment from CBS News.
Billboard and the Times both say it could be the biggest such deal ever.
Springsteen would be the latest star to sell all or parts of their catalogs following, among others, Bob Dylan, Stevie Nicks, Paul Simon, Shakira and Neil Young,
There's been a purchasing boom for song rights. Investors have been increasingly drawn to the lucrative portfolios due to the rise of streaming and, as the Times puts it, "a promise of growing music revenues for years to come."
Last year, Dylan sold his full publishing catalog for a reported sum of $300 million to Universal Music Publishing Group, while Fleetwood Mac's Nicks sold a majority stake in her catalog, reportedly for $100 million.
Springsteen, 72, has been with Sony's Columbia Records for his entire 50-year career, selling more than 150 million records.
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