In March 1988, Iraqi jets swooped over the village of Halabja and sprayed it with a deadly mix of mustard gas and the nerve agents Tabun, Sarin and VX.
Three-quarters of the victims in the five-hour assault were women and children. It is thought to have been the deadliest gas attack ever carried out against civilians.
Dabbagh said in a statement that al-Majid was not subjected to any abuse during the execution, unlike when Saddam Hussein was hanged in December 2006.
Al-Majid was first sentenced to hang in June 2007 for his role in the military campaign against ethnic Kurds, which took place between February and August 1988.
Josh Rushing, Al Jazeera's correspondent in Irbil, northern Iraq, said: "We've stopped and talked to a number of Kurds, and they are quite happy that Chemical Ali got what he deserved and justice was served."
In December 2008, he received another death sentence, this time for his part in crushing a Shia revolt after the 1991 Gulf War.
Al-Majid was sentenced to death again in March 2009 for his role in killing and displacing Shia Muslims in 1999, then for a fourth time in January this year for the 1988 gas attack that killed around 5,000 Kurds.
Iraq's presidency council approved his execution at the end of February 2008, but legal wrangling held up the execution.
Al-Nasr Dureid, an MP candidate for the Iraqi National Movement, told Al Jazeera: "He was one of the biggest criminals of the previous regime and we had to deal with him sooner or later.
"Most Iraqis believe that Ali Hassan al-Majid was a criminal and had to pay for what he did to the Iraqi people.
"I dont think that even the most extremist of people in Iraq believe that Ali Hassan al-Majid deserved any mercy of any kind."
Rise to power
Al-Majid owed his rise in Iraq's government to his cousin and president, Saddam Hussein, who came to trust few beyond his Sunni Muslim clan based around Tikrit, north of Baghdad.
He played a key role in the purge of the Baath party in 1979, when Saddam, formally installed as head of state, sat on the stage of an auditorium and watched "traitors" being led away to their deaths after their names were called out.
In August 1990, after the invasion of Kuwait, Saddam had appointed him military governor of what was deemed to be Iraq's "19th province", but replaced him three months later for fear his brutal reputation was strengthening the hand of Kuwait's allies.
When a US-led coalition expelled Iraqi forces from Kuwait in 1991, Saddam appointed al-Majid interior minister to help stamp out the Shia rebellion sweeping southern Iraq.