The Populus survey, commissioned by campaign group Dignity in Dying Scotland, found 87 per cent backed the move for terminally ill people with less than six months to live, with medical approval and safeguards.
Just 8 per cent of people were opposed while the remainder said they did not know.
The results, from a survey of 1,057 adults last month, were released as the campaign group starts a national advertising drive calling on people to help legalise assisted suicide.
Campaigners want the Scottish Parliament to legislate to allow terminally ill, mentally competent adults to have the choice of an assisted death.
READ MORE: Most Scots would trust their GPs to advise them on assisted dyingPeople with terminal illnesses who back assisted dying and those who have lost loved ones who would have chosen the option if it were legal in Scotland feature in the campaign.
Liz Wilson, 45, from Cumbernauld is one of those taking part.
Her husband Craig died from cancer in December and she said had "begged" to go to Switzerland where assisted dying is legal but was unable to travel.
She said: "Craig was only 45 when cancer took over his whole body. It was horrific to watch him suffer in the way he did. No amount of palliative care could help him.
"For Craig, while he was dying a minute was like an hour and a day like a year. He begged to go to Switzerland but it was sadly too late."
She added: "I don't believe anyone should have to go through what Craig did. I have promised to campaign to change the law so no-one else has to."
Dawn Morton, 34, from Dunfermline also features in the campaign.
She was diagnosed with motor neurone disease in 2014 and now needs 24-hour ventilation and care.
Ms Morton wants to be able to choose assisted suicide to spare her six-year-old daughter Abigail from watching her die in pain.
She said: "I couldn't afford to go to Switzerland and it is important to me to be around as long as possible for my daughter, but I don't want her to see me die badly and in pain.
"I wish the choice of assisted dying was available in Scotland so I could decide when the time was right for me."
READ MORE: ‘Watching my husband die was horrendous’ - Edinburgh widow calls for assisted dyingDignity in Dying Scotland director Ally Thomson said: "Most Scots believe that dying people should not be forced to suffer at the end of life and that there are currently too many bad deaths.
"Their views cannot be ignored. The law in Scotland needs to change."
She added: "This campaign is all about love and putting the voice of people who have lived and are living through the injustice of the current law at the heart of the debate."
A cross-party group of nine MSPs recently joined together to call for assisted suicide to be legalised in Scotland.
Previous attempts to change the law at Holyrood have failed.
Chief executive of the Care Not Killing umbrella group opposing assisted suicide, Gordon Macdonald, said: "The last time MSPs voted on the issue of assisted suicide, they rejected Patrick Harvie's Assisted Suicide Bill by 82 to 36.
"Most members realised then that the risks of legalising assisted suicide were too high and would put vulnerable people at risk of harm to justify taking that step."
He said instead of "encouraging suicide" more money should be made available for palliative care.