Paul Lamb, 58, from Leeds, has joined forces with the family of Mr Nicklinson, who died in 2012.
Earlier this year, Nr Nicklinson’s widow Jane won permission to continue the challenge to a High Court ruling against doctor-assisted death.
Anti-euthanasia campaigners say the current law protects vulnerable people.
The two cases will be heard in the Court of Appeal on 14 and 15 May.
In England and Wales, it is an offence to encourage or assist a suicide or a suicide attempt. The law is almost identical in Northern Ireland.
In Scotland there is no specific law on assisted suicide, although in theory someone could be prosecuted under homicide legislation.
BBC legal correspondent Clive Coleman says Mr Lamb’s case goes beyond assisted suicide, because he is so badly paralysed that he could not take the final steps to kill himself.
He would need a doctor to kill him, which would amount to murder, our correspondent says.
In March, the Court of Appeal granted an order allowing Mr Lamb, who has waived his right to anonymity, to take over Mr Nicklinson’s claims.
He is seeking a court declaration that any doctor who killed him would have a defence against such a charge.
The defence is known as “necessity”, meaning it was necessary for the doctor to act to stop intolerable suffering.
Mr Lamb, who was severely injured in a car accident in 1990, has no function in any of his limbs apart from a little movement in his right hand. He says he has been in pain for 23 years, needs 24-hour care and his life consists of “being fed and watered”.
In a statement to the courts, he said: “I am in pain every single hour of every single day. I have lived with these conditions for a lot of years and have given it my best shot.
“Now I feel worn out and I am genuinely fed up with my life. I feel I cannot and do not want to keep living. I feel trapped by the situation and have no way out.
“I am fed up of going through the motions of life rather than living it. I feel enough is enough.”
Mr Lamb, a divorced father of two, said he was not depressed and just wanted to end his life in a dignified way, with his loved ones around him.
Threat to vulnerable people
However, Dominica Roberts, from the campaign group Care Not Killing, said “it would be very dangerous to give [doctors] the authority to kill”.
She said there was a very small number of “very firm-minded people”, such as Mr Nicklinson and Mr Lamb, who want the law changed, “but on the other side you have… perhaps hundreds of thousands of vulnerable people whom the law protects by the absolute blanket ‘thou shalt not kill’.”
She described the Lamb and Nicklinson legal action as “an attack on the law against murder”.
“It is after all pretty much the most basic law that we have, that you shouldn’t murder people.”
Disability rights group Scope also raised concerns about the risk to disabled people if legislation were changed.
Scope chief executive Richard Hawkes said: “We must avoid any temptation to change assisted suicide laws based on a couple of undeniably heart-wrenching and tragic cases.
“Many disabled people are against any weakening of the law, and their voices need to be heard in this debate.”
In January, Mrs Nicklinson won permission to continue her husband’s campaign and appeal against the High Court ruling that refused to grant him permission to seek medical assistance to die.
Mrs Nicklinson told BBC Breakfast: “In my mind the severely disabled are being blatantly discriminated against. Why shouldn’t they have the same rights as everyone else? There would obviously be huge safeguards put in place so that people are protected.”
Mr Nicklinson was paralysed from the neck down after a stroke in 2005 and suffered from locked-in syndrome. After refusing food and fluids, the father-of-two died from pneumonia at his home in Melksham, Wiltshire, on 22 August 2012.
He was one of several people to challenge the current laws on assisted dying. Diane Pretty, who was terminally ill with motor neurone disease and died in 2002, wanted the courts to give her husband immunity from prosecution.
Debbie Purdy, who has severe multiple sclerosis, challenged the lack of clarity on the law on assisted suicide. She wanted to understand how prosecutors would make a decision on whether or not to prosecute her husband if he were to assist her to get to Switzerland to be helped to die.
Ms Purdy won her case and guidance was issued in 2010, but the law did not change.