The right-to-die campaigner from Melksham, who suffered from locked-in syndrome, has died at home.
Lawyers for the father of two said he died at his home in Melksham, Wiltshire, at around 10am on Wednesday.
Family solicitor Saimo Chahal said: "I am extremely sad to tell you that I received a call at 10.45am from Jane Nicklinson to inform me that her husband Tony died peacefully at home at abour 10am this morning.
"Jane told me that Tony went rapidly downhill over last weekend, having contracted pneumonia.
"He had made an advanced directive in 2004 refusing any life-sustaining treatment and also refused food from last week.
"Jane said that, after Tony received the draft judgement on August 12 refusing his claim, the fight seemed to go out of him.
"He said that 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."
The statement added that Mr Nicklinson died with his daughters, wife and sister Ginny by his side.
A tweet posted on his Twitter page 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, posting on her personal Twitter profile, wrote: "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."
Last week, the High Court rejected Mr Nicklinson's legal battle for the right to die with medical help.
His wife Jane described the decision as "one-sided", and said at the time they intended to appeal.
A spokesman for Wiltshire Police said the force would not be investigating his death.
"Police are not involved at all. We can confirm he passed away and it is not a matter for Wiltshire Police," he said.
"His death certificate has been signed by a doctor, so it is not a matter for Wiltshire Police or the coroner."
Mr Nicklinson was left paralysed by a catastrophic stroke while on a business trip to Athens in 2005.