The author, who has Alzheimer's, says he wants a tribunal set up to help those with incurable diseases end their lives with help from doctors.
A poll for BBC One's Panorama suggests most people support assisted suicide for someone who is terminally ill.
Sir Terry is due to set out his ideas in Monday's Richard Dimbleby lecture. In the keynote lecture, Shaking Hands With Death, the best-selling author will say that the "time is really coming" for assisted death to be legalised.
God's waiting room
His comments follow the acquittal last week of Kay Gilderdale, who was cleared of attempted murder after helping her daughter, Lynn, to commit suicide.
Lynn was found dead at their home on 4 December 2008.
Ms Gilderdale is to appear in Monday's BBC One Panorama programme.
A survey for the programme found 73% of those asked believed that friends or relatives should be able to assist in the suicide of a loved one who is terminally ill.
Sir Terry says he would like to see measures put in place to ensure that anyone seeking to commit suicide was of sound mind and not being influenced by others.
A legal expert in family affairs and a doctor familiar with long-term illness would also be part of his proposed tribunals.
"It seems sensible to me that we should look to the medical profession that over the centuries has helped us to live longer and healthier lives to help us die peacefully among our loved ones in our own home without a long stay in God's waiting room," he will say.
More than 1,000 people were surveyed for the poll carried out for Panorama.
While there was clear support for assisted suicide for someone who is terminally ill, if - as in the case of Ms Gilderdale's daughter - the illness is not terminal, support for assisted suicide falls to 48%.
Responding to the Panorama poll, Director of Care Not Killing, Dr Peter Saunders, said: "To argue that if you are terminally ill you deserve less protection from the law than do the rest of us is highly discriminatory as well as dangerous.
"Many cases of abuse involving elderly, sick and disabled people occur in the context of so-called 'loving families' and the blanket prohibition of intentional killing or assisting suicide is there to ensure that vulnerable people are not put at risk."
Lynn was bedridden by the age of 15, and was admitted to hospital more than 50 times with a succession of serious illnesses over the next 16 years.
Ms Gilderdale told the programme: "I know I did the right thing for Lynn. She's free and at peace where she needed to be. Whatever the consequences, I would do it again."
The survey was carried out earlier this month and the figures are broadly in line with previous surveys.
Last year, the director of public prosecutions issued guidelines on when assisted suicide cases should be taken to court.
But campaigners have said there still needs to be more clarity in the law.
I like the fact that he's including measures to ensure that the person ending their life isn't under pressure to do so- that's one of my only worries about a system in which euthanasia is legalised, and safeguards against it are rarely mentioned. What do you guys think of the plan?