Retired engineer Douglas Sinclair suffered from the debilitating disorder multiple system atrophy and was being cared for at a care home in Jarrow, South Tyneside, when his condition got worse.
The father-of-one is believed to have travelled to an assisted suicide clinic in Zurich, where he died around five weeks ago.
A death notice in the Shields Gazette newspaper said Mr Douglas, a widower, died "peacefully and with dignity following an illness courageously borne".
Northumbria Police said: "A 47-year-old woman and a 48-year-old man from South Shields have been arrested on suspicion of intentionally doing an act to assist or encourage suicide following the death of a 76-year-old man in Switzerland.
"Both have been bailed pending further inquiries."
Former neighbour Joe Bolam, 68, of Highfield Drive, South Shields, said Mr Sinclair was well-known in the area, where he had lived for more than 30 years.
Mr Sinclair's wife Monica died 10 years ago from leukaemia.
Mr Bolam believed he went into a care home last year as his condition worsened.
He said: "He was a smashing bloke. When we heard what happened, everyone was devastated."
Mr Bolam said he believed people should have the right to decide when to die.
"I think it should be legal if it is a person's wishes," he said.
"It is a horrendous condition that he had."
Northumbria Police will investigate the events leading to Mr Sinclair's death and the decision whether to charge anyone will be made by the Director of Public Prosecutions, the most senior figure in the Crown Prosecution Service.
It was believed the two people took legal advice before Mr Sinclair travelled to Switzerland.
Solicitor Chris Potts, of the firm Patterson, Glenton and Stracey, accompanied them during their police interviews after they were arrested.
He said: "They have explained what they did or did not do to police. It would be inappropriate to comment beyond that.
"Both were interviewed under caution, both co-operated fully, they answered each question. They gave every co-operation to explain the events.
"The police have been very sensitive and have approached the case with an open mind. Their task is to collate the information and offer it upwards to the CPS and the DPP. That will take months, not weeks."
Mr Potts said the two people do not want to speak publicly about the case while the police investigation is under way.
In February the DPP published guidelines on assisted suicide cases which outlined public interest factors to be considered for and against each prosecution.
Among the factors against prosecution were whether the suspect was motivated by compassion, and whether he or she had co-operated with investigators.
According to the Multiple System Atrophy Trust, the early stages of the condition are similar to Parkinson's disease.
The progressive neurological disorder strikes men and women typically in their 50s and 60s, and affects different areas of the brain that control the body's functions.
Symptoms may include stiffness and mobility problems, slurred speech, lack of bladder control, difficulty swallowing and choking.
Pressure group Dignity in Dying said the tragedy strengthened its argument for a change in the law on assisted death.
Chief executive Sarah Wootton said: "This is yet another tragic case of a terminally-ill adult being forced to travel abroad in order to have an assisted death, and is a sad reminder of how our current law is failing dying patients and their loved ones.
"While it is likely that people accompanying a relative or friend abroad to die will be acting out of compassion, it is important that cases of assisted dying are investigated, despite this currently having to be a retrospective investigation, after the person has died.
"Much better would be an assisted dying law with upfront safeguards, which would investigate a request to die when the person is still alive and alternative options can be set out.
"This would better protect potentially vulnerable people, provide choice at the end of life for those suffering unbearably and prevent those who act compassionately towards another's request to die from lengthy and distressing investigation whilst grieving for the loss of a loved one."
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