The most comprehensive and recent publication I've found related to this question is The relationship between cognitive ability and chess skill: A comprehensive meta-analysis. It's behind a paywall, but you may be able to find copies of the PDF by googling the title. Also here's a less technical overview of the article from ScienceDaily.
The bottom line is that according to a meta-analysis of numerous studies, there is clearly a correlation between chess skill and cognitive ability, but cognitive ability explains only about 6% of the variance in chess skill (12% if you only consider numerical ability only). There must be other factors as well (e.g., training), some of which could be more important than cognitive ability.
An interesting observation was that intelligence plays a bigger role among lower-level players; here's a relevant quote from the ScienceDaily article.
The study found that intelligence was linked to chess skill for the
overall sample, but particularly among young chess players and those
at lower levels of skill. This may be because the upper-level players
represent a winnowed distribution of cognitive ability -- in other
words, they all tend to be fairly bright. (By way of comparison,
Burgoyne said, consider the world's best basketball players. Although
there is essentially no correlation between height and points scored
at that level, that doesn't mean height isn't important in
I don't have an answer specifically regarding the IQ of GMs or world champions, but this page has an interesting, if unsourced, factoid:
International team of psychologists have attempted to measure IQ score of Garry Kasparov and after many tedious tests has concluded Kasparov’s IQ to be 135, making him fall into ‘moderately gifted’ category.
(I later found the same claim in other websites, some of which say that the testing was organized by Der Spiegel in the 1980s.)
If this is true, it would mean Kasparov is perhaps in the top 1% in terms of IQ, which is certainly not bad, but seems almost nothing compared to the percentile he occupies in terms of chess skill (top 0.0001% or whatever, depending on how you define "chess player").