Noel Conway, 67, was diagnosed with motor neurone disease in November 2014. His condition is incurable and he is not expected to live beyond the next 12 months.
Conway, a retired college lecturer, wants a doctor to be allowed to prescribe a lethal dose when his health deteriorates further.
Conway said he wanted to say goodbye to loved ones "at the right time, not to be in a zombie-like condition suffering both physically and psychologically".
But any doctor who helped him to die would face up to 14 years in prison.
Conway told the BBC: "I will be quadriplegic. I could be virtually catatonic and conceivably be in a locked-in syndrome - that to me would be a living hell. That prospect is one I cannot accept."
Conway was once fit and active but motor neurone disease is gradually destroying all strength in his muscles.
He cannot walk and increasingly relies on a ventilator to help him breathe. As his disease progresses, he fears becoming entombed in his body.
Conway is too weak to come to court from his home but his lawyers will say he wants the right to a peaceful and dignified death while he is still able to make the decision.
Conway is being supported by the campaign group Dignity in Dying.
The last major challenge to the law was turned down by the Supreme Court three years ago.
It ruled that while judges could interpret the law it was up to Parliament to decide whether to change it.
In 2015, MPs rejected proposals to allow assisted dying in England and Wales, in their first vote on the issue in almost 20 years.
Supporters of the current legislation say it exists to protect the weak and vulnerable from being exploited or coerced.
Last week several hundred supporters staged a protest on a Thames river boat outside the Houses of Parliament.
Afterwards Conway said: "In the past months I have been struck by the number of people who, like me, want the right to choose how we die.
"Today has shown the huge strength of feeling of people who want the right to a dignified death," the Guardian quoted Conway as saying.
The UK's High Court is to begin hearing the legal challenge this week, the report said.