Nguyen Tuong Van was hanged at the city-state's Changi prison just before dawn.
Within minutes, a large church bell in Nguyen's home city of Melbourne tolled 25 times - once for every year of his life.
The hanging follows weeks of campaigning by his family and civil rights groups to stop the execution.
Nguyen, who was born in a refugee camp in Thailand, was described by lawyers in his final hours as calm, resolute and ready to die.
Thousands of people gathered in Australia to pray for Nguyen while Singapore activists moved in pairs overnight to light candles at the prison.
Public gatherings of more than four people require a police permit in the tightly controlled
"I hope the strongest message that comes out of this ... is to the young of Australia. Don't have anything to do with drugs, don't use them, don't touch them, don't carry them, don't traffic in them," Australian Prime Minister John Howard said.
"I have told the prime minister of Singapore that I believe it will have an effect on the relationship on a people-to-people, population-to-population basis"
Australian Prime Minister
Speaking to Melbourne radio station 3AW he said he believed the execution would have a impact on bilateral relations.
"I have told the prime minister of Singapore that I believe it will have an effect on the relationship on a people-to-people, population-to-population basis," he said.
However, he went on to add: "The government itself is not going to take punitive measures against the government of Singapore."
Some 420 people have been hanged in Singapore since 1991, mostly for drug trafficking, an Amnesty International 2004 report said.
That gives the country of 4.4 million people the highest execution rate in the world relative to population.
Diplomacy gave way to frustration this week in Australia, a staunch opponent of capital punishment, as its attorney-general branded Nguyen's impending execution a "barbaric" act.
About 70 people, including Australian politicians, gathered outside the Singapore High Commission in Canberra on Friday with a banner reading "Oh Singapore, how could you?" while
protesters clutching flowers rallied in Sydney and Melbourne.
"The Singapore government had a very hard heart," said the Nguyen family's parish priest, Father Peter Norden, who led a service in Melbourne.
In a tiny concession to Australia, Singapore's prison authority allowed Nguyen to hold hands with his mother before his execution but rejected pleas to let them have a final hug.
Nguyen's twin brother Khoa and a lawyer arrived at the prison at dawn. They could not witness the execution but said they wanted to be as close as possible to him when he died.
His mother Kim was in a Singapore chapel with friends, praying for her son.
"She said to me she was talking to him and able to touch his hair and face. It was a great comfort to her," Nguyen's lawyer Julian McMahon told reporters outside the prison.