He said: "Goodbye world, the time has come. I had some fun."
Mr Nicklinson, 58, died six days after he lost a landmark High Court right-to-die action in which he warned he was condemned to a life of pure torture.
He was left paralysed by a catastrophic stroke while on a business trip to Athens in 2005.
His family said that after receiving a draft of the judgment "the fight seemed to go out of him", and in the past few days the father-of-two suffered rapidly deteriorating health when he contracted pneumonia and refused food.
Mr Nicklinson died at his home in Melksham, Wiltshire, with his wife Jane, daughters Lauren and Beth and sister Ginny by his side.
A message posted on Mr Nicklinson's Twitter profile said: "You may already know, my Dad died peacefully this morning of natural causes. He was 58."
Mrs Nicklinson tweeted: "I have lost the love of my life, but he suffers no more."
Daughter Beth posted on the social networking site: "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."
Her sister Lauren added: "Dad, you are finally at peace. Beth and I are so proud to be your daughters, we got our strength from you. I love you xxx."
Wiltshire Police said there were no suspicious circumstances surrounding the death.
Mr Nicklinson's lawyer, Saimo Chahal of Bindmans LLP, said: "Jane told me that Tony went rapidly downhill over last weekend, having contracted pneumonia.
"He had made an advance directive in 2004 refusing any life-sustaining treatment and also refused food from last week.
"Jane said that after Tony received the draft judgment on August 12 refusing his claim, the fight seemed to go out of him.
"He said he was heartbroken by the High Court's decision that he could not end his life at a time of his choosing with the help of a doctor."
Ms Chahal said Mr Nicklinson told her: "So, we lost. In truth I am crestfallen, totally devastated and very frightened. I fear for the future and the misery it is bound to bring."
Ms Chahal added: "I would like to say what an extraordinary man Tony was. He was gutsy, determined and a fighter to the end.
"I only wish the outcome of the case could have been different during Tony's lifetime."
Ms Chahal warned that the legal battle Mr Nicklinson had so bravely fought would come to an end with his death, unless someone stepped forward.
Lawyers for a man known only as "Martin", who lost his case alongside Mr Nicklinson last week, announced they were to appeal the court's decision.
They said the ruling denied their 47-year-old client "the opportunity to take the necessary steps to end his own life".
Martin, who also suffers from locked-in syndrome, said in a statement: "I am relieved for Tony and offer my condolences to his family for the man they'll miss.
"I hope that I too can be set free from this existence, but I would like it to be in the manner of my choosing."