Officials say the amount of drugs Tochi was carrying was worth about US$980,000.
Malachy was convicted as the man to whom Iwuchukwu was supposed to deliver the drugs.
"The appeals of both Tochi and Malachy to the Court of Appeal and to the President (S.R. Nathan) for clemency have been turned down. Their sentences were carried out this morning at Changi Prison," the Central Narcotics Bureau said in a statement on Friday morning.
Activists had been lobbying the government to halt Tochi's execution, but expressed shock Malachy was also hanged as there had been no word on his case.
"I'm surprised. From what I have heard from... other people, Malachy was not supposed to hang. I was not expecting it," Chee Siok Chin, a campaigner against capital punishment, told AFP.
"We have a duty to safeguard the interests of Singaporeans, and protect the many lives that would otherwise be ruined by the drug syndicates"
Lee Hsien Loong,
Singapore prime minister
Olusegun Obasanjo, the Nigerian president, was among those who had sought clemency for Tochi.
In a letter to Obasanjo, Lee Hsien Loong, Singapore’s prime minister, said that while some people might find the hanging hard to accept, "We have a duty to safeguard the interests of Singaporeans, and protect the many lives that would otherwise be ruined by the drug syndicates."
Lee said the amount of heroin that Tochi was convicted of carrying was equivalent to more than 48,000 doses - "enough to have destroyed many lives and families".
But, according to the United Nations' Human Rights Council, the hangings violate the international legal standards on the use of the death penalty.
Philip Alston, an Australian lawyer who reports to the council, said death penalties may only be imposed if the evidence "left no room for an alternative interpretation of the facts".
At the time of his arrest, Tochi told narcotics officers the pills were African herbs that he was supposed to give to a sick friend. He also told officers that he came to try out for soccer teams playing in the Singapore League.
"The reality is that drug trafficking has not been reduced to zero, neither has drug use"
Lee Weng Choy,
death penalty opponent
A small group of opponents to the death penalty gathered before dawn on Friday to light candles and await the execution hour. A red football jersey was hung on the prison fences to mark Tochi's love for football.
Condemning the hanging, Lee Weng Choy, a prominent Singapore-based art critic, said Singapore’s mandatory death sentence had failed to act as an effective deterrent.
"The reality is that drug trafficking has not been reduced to zero, neither has drug use," he said at the vigil.
Tochi’s family, who live in Nigeria, could not afford to travel to Singapore to see him while he was on death row, according to an official at the Nigerian embassy in Singapore.
With a population of 4.4 million Singapore has the highest per capita execution rate in the world, according to human rights group Amnesty International, having hanged more than 420 people since 1991.
Singapore does not make statistics on the death penalty publicly available.