Liam McArthur, who is bringing forward a bill which would allow terminally ill and mentally competent adults to end their lives, said it was "absolutely the right time" for the move.
In an interview with Scotland on Sunday, he said there had been a "gradual shift in terms of the political mood catching up with where the public mood is".
The Liberal Democrat MSP said: "The argument is made that tough cases make bad law, but bad law also creates tough cases. It works both ways.
"It seems to me that we've reached a point where this is not going to go away.
"In some senses, it's likely to get worse and we do need to address it."
Mr McArthur said the ability to prolong life "is likely to continue to expand" due to "fantastic" advances in medicine.
He added: "But I think the more we see those medical advances, the more the potential is that in a sense we're able to prolong life in ways that may not be desirable for individuals in their own circumstances.
"But alongside this, I absolutely believe there needs to be a debate around how we further develop, and probably more particularly expand the access to palliative care and specialist palliative care."
Mr McArthur's bill is the third attempt to legalise assisted dying in Scotland, and he argues it contains "strong safeguards".
Two doctors would need to confirm a person was terminally ill and mentally competent, and there is a suggested reflection period of 14 days.
Mr McArthur said the proposals are "pretty tightly drawn" and do not go as far as previous plans.
He is hopeful the legislation will be introduced later this year, and believes MSPs will back it, making Scotland the first place in the UK to legalise assisted dying.
The Orkney MSP, who is also a deputy presiding officer of the Scottish Parliament, said two elections have passed since Holyrood last considered such plans.
He thinks the country will "very quickly come to the point of wondering how on earth it took us quite so long".
He added: "The longer I've been involved in this, the more convinced I've become that a change in the law is not just necessary, it's long overdue.
"And what I need to guard against is trying to rush this through because I believe it's long overdue and it's much needed, and that there are those who could benefit from it who won't because we won't have passed the law in time for them to avail themselves of it.
"Because we absolutely need to get this right."
Some MSPs have already raised concerns. Labour's Pam Duncan-Glancy, a permanent wheelchair user, called the proposals "dangerous for disabled people".
Mr McArthur said he has had a "lengthy conversation with Pam", adding: "I'm not necessarily convinced that I'm going to be able to persuade her to change a position she's had on this issue for many, many years.
"I think what I'm more keen to do is understand the basis of the concerns she has, and make sure that as far as possible those can be addressed in the framing of the legislation."
He said he would be keen to meet with any MSP who has concerns.
Mr McArthur said the current law leaves individuals and family members in a "pretty invidious" position, adding: "That just seems to compound an already horrendous situation."
He said: "I do see this as the next big liberal reform, and for a country like Scotland, with the aspirations we have in the modern world, it seems to me that it's absolutely the right time.
"It will be highly significant. I think it will be a landmark piece of legislation if it's passed."
A consultation on the bill closed in late December after receiving an "unprecedented" response.
Mr McArthur cites examples of individuals and families watching loved ones die “a needlessly protracted and undignified death”.
He remembers sitting in Holyrood during an earlier debate led by Jeremy Purvis, a Liberal Democrat MSP between 2003 and 2011.
Those making the argument for change "seemed to be doing something that felt quite politically courageous".
Mr McArthur said it feels “much less risky now”.
He said: "This seemed to me to be an issue that we will need to find a better resolution to than just saying, no, the status quo is adequate.
"I think the advances we're seeing in medicines, the advances we're seeing in palliative care, are throwing up all sorts of different choices and options and scenarios that were perhaps inconceivable not that long ago.
"And I think as we're seeing more countries, more states within countries, taking forward legislation of their own, it gives us, I think, an opportunity to look at the evidence of how that works in practice.”
Gordon Macdonald, chief executive of Care Not Killing, which opposes the legislation, has raised numerous concerns.
He said: “Changing the law to legalise assisted suicide in Scotland would represent a dramatic change in how doctors and nurses treat and care for people.
"It would also place huge pressure, real or perceived on terminally ill and disabled people to end their lives exactly as we see in the handful of places that have legalised assisted suicide or euthanasia.”
Mr Macdonald added: “It is disappointing at time when we have seen widespread discrimination against the elderly and disabled people, along with a crisis in the NHS and care system that we continue to ignore the more important debate of how to extend high quality palliative care to all those who need it.”