The 64-year-old record producer - who was a personal friend of Chris and his wife Vicky Karayiannis - described the Soundgarden and Audioslave frontman as a ''great artist''.
Above a picture of Chris and himself stood side-by-side, Nile wrote on Twitter: ''A mutual friend called me and tells me my bro passed away. #RIPChrisCornell You are a great artist Love to Vicki and fam @nilerodgers (sic)''
Nile also extended his condolences to Vicky and their children Toni, 12, Christoper, 11, and Lillian, 16, via Instagram.
He wrote on the photo-sharing website: ''#RIPChrisCornell My heartfelt condolences to Vicki and your family. You are my special brother @nilerodgers (sic)''
Led Zeppelin rocker Jimmy Page has also paid tribute to Chris, describing him as an ''incredibly talented'' artist.
Writing on Twitter, Jimmy said: ''RIP Chris Cornell Incredibly Talented Incredibly Young Incredibly Missed. (sic)''
Elsewhere, Bush frontman Gavin Rossdale said he was in ''total shock'' after hear of his passing.
Gavin tweeted: ''I AM SO SADDENED BY CHRIS CORNELL PASSING. @ soundgarden TOTAL SHOCK.GREAT MAN.GREAT BAND.GREAT LOSS. LOVE TO EVERYONE IN HIS WORLD. XXX (sic)''
Meanwhile, Mike Portnoy, the co-founder of rock band Dream Theater, said the news of Chris' death was ''shocking''.
He wrote on the micro-blogging site: ''Wow...this one is shocking. Chris Cornell was one of the benchmark vocalists of our generation...devastating loss. #RIPChrisCornell (sic)''
Mike subsequently posted a screenshot of the cover of Chris' track 'Follow My Way' from his 1999 album 'Euphoria Morning'.
He captioned the image: ''Crazy...just a few days ago, this came up on my iTunes Shuffle and I was floored by the songwriting #RIPChrisCornell (sic)''
Chris passed away shortly after he performed a sold-out concert with Soundgarden at Fox Theatre in Detroit, Michigan.
Medical tests are set to be conducted to establish the reason for the rock star's sudden death.
A statement issued to BANG Showbiz confirming the sad news read :''Chris Cornell passed away late Wednesday night in Detroit, MI. His wife Vicky and family were shocked to learn of his sudden and unexpected passing, and they will be working closely with the medical examiner to determine the cause. They would like to thank his fans for their continuous love and loyalty and ask that their privacy be respected at this time.''