Some critics in Switzerland say assisted suicide should only be available to the terminally ill.
He did not have a terminal illness but his quality of life had deteriorated in recent years. The death occured at 1030 GMT from an infusion of Nembutal, a barbiturate, at the Life Cycle clinic, he said.
In 2016, aged 102, he won a battle to keep working on campus at Perth's Edith Cowan University, where he was an unpaid honorary research associate.
"I would like being able to walk in the bush again, also see what is about me", added the father of four, who during his long life had three sisters.
The best-known group to help foreigners end their lives in the Alpine country is Dignitas, but others include Life Circle in Basel, Mr Goodall's choice.
Dr Goodall ate his favourite dinner of fish and chips, followed by cheesecake, for his last meal on Wednesday evening, Dr Nitschke said.
Under Swiss law, a person with "commendable motives" may not cause another person's death, and a person with "selfish motives" may not assist in the death; but the law does not forbid a person with "commendable motives" from assisting someone in taking their own life.
The Netherlands, Belgium and Luxembourg permit euthanasia and assisted suicide.
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"There's not going to be many people who have either the ability or the money or the willingness to go through what is quite a long and hard journey", Dr Nitschke said from Switzerland. Starting in June 2019, terminally ill patients who have a life expectancy of less than six months can request a lethal drug to end their lives.
"My abilities have been declining over the past year or two. What's the use of that?" said the scientist, who appeared to have lost none of his sense of humor on Tuesday, wearing a top inscribed with the words "Aging Disgracefully".
Meanwhile, Switzerland has allowed assisted suicide since 1942.
Modern medical practice is very focussed on curing people but struggles to confront the suffering where death is inevitable and unavoidable.
Sky's Michelle Clifford said police and coroner officials would now need to visit the clinic to make sure the assisted suicide was carried out properly.
"The process of dying can be rather unpleasant, but it need not be", he said. "The message I would like to send is: Once one passes the age of 50 or 60, one should be free to decide for oneself, whether one wants to go on living or not".