The deal, completed last July, includes everything from classic 1960s albums like Blonde On Blonde, up to his latest release, 2020's Rough And Rowdy Ways.
Billboard magazine says the catalogue is worth about $200m (£149m), based on annual revenues of roughly $16m (£12m).
Dylan previously sold his publishing to Universal Music for a reported $400m.
That deal covered the rights to Dylan's lyrics and compositions, which Sony had previously administered outside the US.