On the rock'n'roll scene since the age of 15, Keys played with Buddy Holly, John Lennon and Eric Clapton.
The 70-year-old was most famous for his work with the Stones on the classic track Brown Sugar and their album Exile On Main Street.
The band issued a statement mourning "the loss of their very dear friend and legendary saxophone player".
The statement went on: "Bobby made a unique musical contribution to the band since the 1960s. He will be greatly missed."
Guitarist Keith Richards said: "I have lost the largest pal in the world and I can't express the sense of sadness I feel although Bobby would tell me to cheer up."
Keys featured in Richards' autobiography Life in 2010 and recalled the first time he met the Stones in the mid-1960s.
Like Buddy Holly, Keys was born in the Texas town of Lubbock and had toured with him and his band The Crickets in the 1950s.
But he was not impressed that the Stones had recorded a cover of Buddy Holly's Not Fade Away.
Keys recalled the moment: "I said 'Hey, that was Buddy's song. Who are these pasty-faced, funny-talking, skinny-legged guys to come over here and cash in on Buddy's song?'''
Keys played during the band's Glastonbury headline slot in 2013, although in October he was forced to pull out of dates in New Zealand and Australia due to poor health.
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The 27-year-old spent last season on loan at Chesterfield, scoring 15 goals in 38 appearances for the Spireites.
Novak has agreed a three-year contract at The Valley and becomes the Addicks' third signing of the summer.
"Lee has shown a consistency at both Championship and League One level and is a proven goalscorer," Charlton boss Russell Slade told the club website.
Novak joined Birmingham from Huddersfield in summer 2013 and scored 12 goals in 69 outings for the Blues.
Meanwhile, Charlton striker Igor Vetokele has joined Belgian Pro League side Zulte-Waregem on a season-long loan deal.
Zulte-Waragem have an option to buy the 24-year-old Angola international as part of the deal.
Vetokele moved to south-east London in the summer of 2014 and scored two goals in 18 appearances in 2015-16.
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Olsson, who played 261 times after joining the Baggies in 2008, would have been out of contract this summer.
But the Premier League club have agreed to cancel his deal early so he can return to his homeland in time for the start of their new top-flight season.
"Albion has, and will always be, a huge part of my life," said Olsson, 34.
"It's all happened so quickly I've not had chance to say a proper farewell to so many people. I will be back at the first chance to do that.
"I'm really grateful to the club for helping me sort out this transfer," said the Swede, who also captained Albion during his near nine years' service to the club.
Meanwhile, teenager Kane Wilson has signed his first professional contract at The Hawthorns, the 17-year-old defender having signed a deal which ties him to Albion until the summer of 2019.
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The Rolling Stones say they're devastated over the death of Bobby Keys, who played saxophone for them.
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League One side Charlton Athletic have signed Lee Novak following the striker's departure from Birmingham.
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West Bromwich Albion's long-serving defender Jonas Olsson has had his contract cancelled to allow him to move back to Sweden to join Djurgarden IF.