Frontman Ozzy Osbourne tweeted: "Geoff Nicholls was a great friend of mine for a long time. He will be greatly missed. I'm very saddened at the news."
And bassist Geezer Butler wrote on Facebook. "Very sad to hear of old friend and Sabbath keyboard player Geoff Nicholls passing. RIP Geoff (sic)."
Geoff joined Black Sabbath in 1979 and the 1980 album, Heaven and Hell was the group's first record that he appeared on.
He left the band in 1996.
Meanwhile, Tony was diagnosed with lymphoma cancer in 2013 and previously admitted he believes his treatment unintentionally forced drummer Bill Ward to leave Black Sabbath.
Recalling receiving the news while recording their 2013 LP 13, he said: "My illness has changed my life a lot and my attitude. When I was going through my treatment, I didn't think I was going to last, I had stage three lymphoma.
"I wanted to get things going quick, and Bill wanted to take longer. Bill seemed to feel he was getting a bad deal. We never dealt with that, we left all that to management. We just wanted to play together and enjoy it. We were playing with Bill for a bit and then he never turned up. I thought, 'what's going on?"