Lead singer Gary Brooker and lyricist Keith Reid always claimed credit for the hit, which became part of the soundtrack for the hippy "summer of love" of 1967.
But in his ruling, the judge decided that organist Matthew Fisher was entitled to both credit and royalties.
"I have come to the view that Mr. Fisher's interest in the work should be reflected by according him a 40 percent share of the musical copyright," the written judgment said. "His contribution to the overall work was on any view substantial but not, in my judgment, as substantial as that of Mr. Brooker."
The judge said the song's organ solo "is a distinctive and significant contribution to the overall composition and quite obviously the product of skill and labor on the part of the person who created it."
The judge said Fisher, 60, was entitled to royalties from May 2005, when he began court proceedings.
"A Whiter Shade of Pale," famous for its cryptic lyrics — "We skipped the light fandango, turned cartwheels 'cross the floor" — topped the British charts for five weeks in 1967 and was a Top 5 hit in the U.S.
Rolling Stone magazine has ranked it 57th in a list of the 500 greatest songs of all time.
Brooker says he and Reid wrote the song before Fisher joined the band in March 1967. It was released in May.
Fisher, now a computer programmer living in south London, left the band in 1969. Brooker, 61, still tours with Procol Harum.
In a statement, Brooker and Reid said Fisher's court victory created a dangerous precedent because it meant any musician who had played on any recording in the past 40 years could claim joint authorship.
"It is effectively open season on the songwriter," they said. "It will mean that unless all musicians' parts are written for them, no publisher or songwriter will be able to risk making a recording for fear of a possible claim of songwriting credit."
They intend to file an appeal.