Another tweet, on behalf of 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.”
In a brief statement, Bindmans LLP said Mr Nicklinson, from Melksham, Trowbridge, died this morning at home.
“This is to notify you of the sad death of Tony Nicklinson at approximately 10am this morning,” the law firm said.
Family solicitor Saimo Chahal added: “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 about 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.”
Wiltshire Police said the force would not be investigating Mr Nicklinson’s death.
A spokesman said: “Police are not involved at all. We can confirm he passed away and it is not a matter for Wiltshire Police.
“His death certificate has been signed by a doctor, so it is not a matter for Wiltshire Police or the coroner.”
You may already know, my Dad died peacefully this morning of natural causes. he was 58.
The married father-of-two was left paralysed by a catastrophic stroke while on a business trip to Athens in 2005.
Mr Nicklinson’s condition meant that while his mental and cognitive functions were unaffected by the stroke, he was paralysed from the neck down, communicating only by blinking when shown letters.
He had asked the court to allow doctors to end his life without the risk of prosecution because his quality of life had deteriorated to such an extent that he was condemned to “a life of increasing misery”.
But the three judges ruled that although Mr Nicklinson’s case raised constitutional issues, presenting society with “legal and ethical questions of the most difficult kind”, it was for parliament to decide on any change to existing laws.
Channel 4 News’s Cathy Newman interviewed Mr Nicklinson last week. Read her story here.