Singapore put a halt to all executions in July 2011 while it reviewed its use of the mandatory death penalty and now allows judges to have more discretion in certain cases.
Last November, it lifted the death penalty on a convicted drug trafficker for the first time.
When the review took place, all people on death row were allowed to ask to be considered for re-sentencing, though the CNB said Tang and Foong both said they did not want to be considered.
"Tang Hai Liang and Foong Chee Peng had been accorded full due process," the CNB said.
The Singapore Working Group on the Death Penalty, a group of non-governmental organisations, said they believed the executions should not have taken place given another drug offender is making a constitutional challenge against the anti-drug laws.
"It was deeply unjust to have executed them before the constitutional challenge was decided," they said in a statement.
"The executions are a regrettable step backwards for Singapore," they added.
Singapore has some of the toughest anti-drugs laws in the world, and its customs forms warn arriving travellers of "death for drug traffickers" in no uncertain terms.
It has hanged hundreds of people - including dozens of foreigners - for narcotics offences in the last two decades, Amnesty International and other groups say.
(Reporting by Rachel Armstrong; Editing by Robert Birsel) - The Star Online, 18/7/2014,Singapore hangs two drug traffickers, first executions in over three years