The suspect said he was enraged by the politician's opposition to laws ordering death for insulting Islam.
Punjab governor Salman Taseer, 66, was a senior member of the ruling party regarded as an outspoken moderate in a country increasingly troubled by extremism.
His assassination on Tuesday added to the turmoil in nuclear-armed Pakistan, where the government is on the verge of collapse and Islamic militancy is on the rise
Yesterday a group of more than 500 Muslim scholars praised the bodyguard and said no one should pray for the governor.
The scholars and clerics group known as Jamat Ahle Sunnat also made a veiled threat against Taseer's supporters in a statement: "The supporter is as equally guilty as one who committed blasphemy."
Prime Minister Yousuf Raza Gilani and other senior ruling party officials joined up to 6,000 mourners at a ceremony at the governor's official residence in the city of Lahore in eastern Pakistan, before Taseer was buried at a nearby cemetery.
Taseer was a close ally of US-backed President Asif Ali Zardari and the highest-profile political figure to be assassinated since former Prime Minister Benazir Bhutto was killed three years ago.
Khusro Pervez, the commissioner of Lahore, said city authorities had deployed additional police to keep the peace. Thousands of police guarded the governor's residence and other key sites.
"Police are on maximum alert. Police are guarding all important installations in the city," Pervez said.
The governor's residence has been the scene of angry street protests in recent weeks against Taseer's call to repeal blasphemy laws that order death for anyone convicted of insulting Islam and his support for a Christian woman sentenced to die for allegedly insulting Islam's Prophet Muhammad.
Taseer was shot in the back in the capital Islamabad as he left a restaurant.
An intelligence official who interrogated suspect, Mumtaz Qadri, said the 26-year-old commando had been planning the assassination since learning four days ago that he would be deployed with security for the governor.
Police were trying to determine how Qadri was assigned to Taseer's security detail and whether he had help.
The official said Qadri said he was proud to have killed a blasphemer.