George Bartlett, 62, fell during maintenance work on the Taqa-operated Harding platform, about 198 miles north east of Aberdeen, at about 2.15am yesterday.
Mr Bartlett, from Shotts, North Lanarkshire, was recovered from the water and airlifted to Gilbert Bain Hospital in Lerwick, Shetland, but later died.
In a statement, his family said: "George was a loving husband, father and grandfather, and will be sorely missed by us all.
"He has worked offshore for many years but, no matter how far away he was, he would always be in touch.
"We are a close-knit family and we now ask that we are given time to come to terms with our loss."
A joint investigation is being carried out by Police Scotland and the Health and Safety Executive and a report will be submitted to the procurator fiscal.
Following the accident, Taqa said production had been suspended on the platform and 74 non-essential staff were being taken off the installation.