All the band's previous records were released by EMI Parlophone, but the Oxford rockers turned down a £3 million offer to renew their contract, according to The Times.
An EMI spokesperson said: "Radiohead were demanding an extraordinary amount of money and we did not believe that our other artists should have to subsidise their gains."
Radiohead's new In Rainbows album is physically released on the XL label today.
The band's manager Bryce Edge has claimed that EMI's refusal to grant the band copyright over their back catalogue, rather than any dispute over payment, was the real reason behind their departure.
Edge commented: "We couldn’t move ahead with EMI because [label boss] Guy Hands irrevocably refused to discuss the catalogue in any meaningful way.
"We sold 25 million records and we have the moral rights over those six albums. We wanted a say in how they are exploited in the future.
"We were not seeking a big advance payment, or a guaranteed marketing spend as discussions never got that far."