The 11 medical experts are backing a Bill proposed by independent MSP Margo MacDonald which would change the law in Scotland.
The Bill will complement the "excellent" palliative care currently on offer in Scotland, not undermine it, they said in a letter.
One of the signatories, ear, nose and throat surgeon Gillian MacDougall, said more GPs support the proposed legislation but fear being labelled "Dr Death".
The letter, published in the Herald newspaper, reads: "We believe the safeguards designed to protect the vulnerable are comprehensive and rigorous, with doctors being the best professionals to assess for any concerns regarding coercion.
"We are also reassured a doctor cannot be compelled to participate in the process, should they not wish to do so.
"As doctors, we support the Assisted Suicide (Scotland) Bill."
The Bill is the second attempt to change the law by Ms MacDonald, who has Parkinson's disease. A previous attempt was voted down by MSPs in 2010.
Under the proposed legislation, only those who are terminally ill or who are suffering from deteriorating progressive conditions which make life intolerable will be able to seek assisted suicide.
Any requests to GPs must be backed up by a second professional opinion and followed by a 14-day ''cooling-off'' period.
This process is then repeated again with a second request, after which one of the doctors concerned would supply a licensed facilitator with a prescription to enable assisted suicide to take place.
This facilitator, or ''friend at the end'', has no relationship with the patient and is given the task of collecting the prescription and agreeing the process of assisted suicide, including whether the person wishes to say goodbye to their family and friends.
If the prescription is not used within 14 days, it must be returned to the chemist.
When she launched the Bill in November, the Lothian MSP said she believed it could be successful this time, stating: ''I have sensed from the beginning that there was a change because of the volume of support that we can demonstrate.''
Dr MacDougall told the Herald: "It is really hard in the medical profession to stand up and say you support this as a practising doctor. I think there is a fear of being labelled Dr Death and fear of any political repercussions."
Another signatory, emeritus professor of medical neurology at Edinburgh University Charles Warlow, said: "I think it is part of one's doctoring responsibility to help someone at the end of life.
"I know many people do that with the double effect of morphine. It is all secretive and it should not be."