Mr Canavan, a former Labour MP who later became an independent MSP, said he had "probably had more than my fair share of deaths in my family".
Four of his children have died, with three having suffered from terminal illness.
However the 79-year-old, who will speak to current MSPs about his experiences at an event in Holyrood on Wednesday, said his children all "died with dignity".
Supporters of assisted suicide often argue that it can give those suffering from terminal conditions a more dignified death, allowing them to die at a time of their choosing.
However, speaking ahead of an event on Wednesday coordinated by Care Not Killing (CNK) campaign group, Mr Canavan said: "I have probably had more than my fair share of deaths in my family, having suffered the loss of four children, three of them as the result of terminal illness.
"However, I found the standard of NHS care to be excellent and the standard of palliative care in our local Strathcarron Hospice was first class.
"My children undoubtedly underwent some pain but it was minimised by caring health professionals.
"As a result, my children died in dignity and I do not accept that the option of assisted suicide is necessary to ensure dignity in death."
Liberal Democrat MSP Liam McArthur is spearheading what is the third attempt to legalise assisted suicide in Scotland, with a proposed Member's Bill.
He wants to make assisted dying a choice for adults who are both terminally ill and mentally competent, and insists there are strong safeguards built into his proposed Assisted Dying Scotland Bill.
Baroness Stephanie Fraser of Craigmaddie, an outspoken opponent of assisted suicide in the House of Lords, will also address Wednesday's meeting.
She recently told how she was "deeply concerned that, with a state-sanctioned way of bringing about the death of the elderly, the unwell and the disabled, criminals and fraudsters would be able to take advantage of the most vulnerable in our society, without fear of consequences".
And CNK chief executive Dr Gordon Macdonald said: "Assisted suicide is a counsel of despair for those suffering serious illness or who are disabled.
"Instead of investing in life enhancing treatments and services, the focus of policy makers becomes on how to help people commit suicide.
"Scottish Government suicide prevention efforts will be undermined with doctors and nurses being asked to facilitate the deaths of some patients whilst working to prevent suicide in other cases."
He continued: "Perhaps most concerning is the risk that people who are vulnerable will come under pressure to end their lives from relatives or healthcare managers who have an eye on the costs of care and would prefer to either to gain a large inheritance or make savings in NHS or social care budgets."
Mr McArthur said afterwards he had "the utmost sympathy for Dennis and the great loss he has had to endure", and added: "I am pleased that the palliative care received by his children was of such high quality and provided relief and comfort."
The Lib Dem continued: "Investment in and access to palliative care is important and for the majority of people it works well to relieve pain at the end of life.
"However, we know that sadly some dying people do go beyond the limits of even the very best care and suffer intolerably as they die.
"The proposals I intend to bring to Parliament work alongside excellent palliative care - giving dying people both excellent care and more choice if they need it.
"The option of a safe and compassionate assisted death would be the choice of the dying person alone and it is a choice that many terminally ill people wish was available to them.
"As this issue progresses through Parliament it is vital that we listen to what dying people are telling us they need to have the death that is right for them."