His comments follow the acquittal last week of Kay Gilderdale, of Stonegate, East Sussex, who was cleared of attempted murder after helping her daughter, Lynn, to kill herself.
Ms Gilderdale admitted aiding and abetting her 31-year-old daughter, who had been battling chronic fatigue syndrome ME for years, to take her own life and was given a 12-month conditional discharge.
Lynn Gilderdale, who had been left paralysed and unable to swallow, was found dead at their home on 4 December 2008.
Sir Terry wants to see measures put in place to ensure that anyone seeking to commit suicide was of sound mind and not being influenced by others.
"At the moment if someone assists someone else to commit suicide in this country or elsewhere they become suspect to murder until the police decide otherwise," he told the BBC.
"I think it would be rather better if a person wishes to die, they could go see the tribunal with friends and relatives and present their case - at least if it happens, it happens with, as it were, authority."
A legal expert in family affairs and a doctor familiar with long-term illness would also be part of his proposed "non-aggressive" 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," Sir Terry said.
More than 1,000 people were surveyed for the poll carried out for Panorama.
It found that 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.
While there was clear support for assisted suicide for someone who was terminally ill, if - as in the case of Ms Gilderdale's daughter - the illness was not terminal, support for assisted suicide fell 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."
Baroness Finlay, an independent peer who is a professor of palliative medicine, told BBC Radio 4's Today it was "hardly surprising" the Panorama poll had found public support for assisted suicide because "opinion polls reflect the way something is presented in the media".
ASSISTED SUICIDE LAWS
The 1961 Suicide Act makes it an offence to aid, abet, counsel or procure a suicide or a suicide attempt in England and Wales
Anyone doing so could potentially face 14 years in prison
Law Lords recently issued new guidelines to clarify this law, spelling out the range of factors that will be taken into account when deciding on cases
The law is almost identical in Northern Ireland
There is no specific law on assisted suicide in Scotland, although someone could be prosecuted under homicide legislation
She said licensing assisted suicide would be a "very dangerous step" because it would remove protection and "suck all sorts of people in".
"Look at what happened in other countries, for instance in Oregon - the number of assisted suicides has gone up fourfold - if that is translated to Britain, we are not talking about a small number, we are talking about a thousand a year," she said.
Baroness Finlay said people had good days and bad days and changed their mind about assisted suicide.
"If you give someone a licence at one point of time, you don't know what will happen after that, there is scope for all kinds of things to happen, like coercion," she said.
If the UK "ever went down that road" it was important legislation fell under the Ministry of Justice, not the Department of Health," she added.
"The difficulty is, if healthcare is part of it, you are actually getting doctors to take shortcuts in care, and with financial measures that's going to mount."
Lynn Gilderdale was bed-ridden 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.
Her mother told Panorama: "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.
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