Overnight his lawyers announced he died at home.
A tweet posted on Mr Nicklinson's profile, which is regularly updated by members of his family on his behalf, read: 'You may already know, my Dad died peacefully this morning of natural causes. he was 58.'
A second post added: 'Before he died, he asked us to tweet: 'Goodbye world the time has come, I had some fun'.'
A third post, attributed to his wife, Jane, and grown-up children Lauren and Beth, said: 'Thank you for your support over the years. We would appreciate some privacy at this difficult time.'
Beth Nicklinson, writing on her personal Twitter profile, paid tribute to her late father. She posted: "RIP @TonyNicklinson. Couldn't have asked for a better dad, so strong. You are now at peace, we will be fine. I love you xxx"
In January, the 58-year-old asked the High Court to declare that any doctor who killed him with his consent would not be charged with murder. Last week, the court rejected his request, a decision that Nicklinson said had left him "devastated and heartbroken."
Nicklinson was a former corporate manager and rugby player who suffered a stroke in 2005 that left him unable to speak or move below his neck. He required constant care and communicated mostly by blinking, although his mind had remained unaffected and his condition was not terminal.
Nicklinson had argued that British law violated his right to "private and family life" as guaranteed by the European Convention on Human Rights, on the ground that being able to choose how to die is a matter of personal autonomy. He had previously described his life as "a living nightmare."
One of his daughters said on her father's Twitter account that he died "peacefully this morning of natural causes." His family said later that he died of pneumonia.
Police said they would not be investigating Nicklinson's death. "We can confirm he passed away," a police spokesman said on customary condition of anonymity. "His death certificate has been signed by a doctor, so it is not a matter for Wiltshire Police or the coroner."
Saimo Chahal, Nicklinson's lawyer, said his health had deteriorated recently and that he was in "a great deal of physical pain and discomfort."
Nicklinson had said that even if he were granted the right to die, he would not want to be killed immediately, but just wanted to know that the option existed.
Experts weren't sure what impact, if any, his death might have on the ongoing euthanasia debate in Britain.
Penney Lewis, a law professor at King's College London, said previous deaths of euthanasia advocates didn't have any effect on changing laws to allow the practice.
"The evidence seems to be that parliaments are not galvanised into action by the deaths of those who have been fighting for (euthanasia) legalisation," she said in an email. Nicklinson "was so distressed by the High Court decision, it is sad to think he died while still absorbing that."
Nicklinson had refused since 2007 to take any life-prolonging drugs recommended by doctors, including heart drugs or blood thinners. His wife, Jane, a trained nurse, had said he could be at risk of another stroke or a heart attack.