Police were sent offshore to investigate after Nichol, an employee of IKM Testing UK, fell ill earlier that day on the vessel in Block 21/25, 185km east of Aberdeen. He died despite receiving medical attention.
The worker was reportedly from Normanby in North Yorkshire, and leaves behind a wife, Ann, and sons Chris and Simon.
"I wish to express my sympathy to the family, friends and colleagues of William Nichol, who sadly passed away on our Anasuria platform, in the central North Sea, on Tuesday evening Shell UK & Ireland's upstream director Paul Goodfellow said.
"We are working closely with Mr Nichol's employer, IKM Testing, to provide support to his family and colleagues during this difficult time."
A spokeswoman for IKM said: "IKM will be supporting [Nichol's] family and his wife Ann and his sons Chris and Simon throughout this difficult time. We wish to extend our sincerest condolences to Mr Nichol's family and friends."
IKM said in the statement to Offshore Energy Today that Shell's emergency response team notified IKM at about 4pm local time that Nichol had collapsed and that, "despite the best efforts of the crew on board, they were unable to revive him".
IKM managing director Tony Perkin said: "Mr Nichol was a dedicated and valued member of the IKM team and will be sadly missed."
Police Scotland confirmed it had been informed of the death, that next of kin had been informed and "inquiries into the circumstances are ongoing".