Police commando Mumtaz Qadri deployed for security of the liberal governor had gunned down Taseer in Islamabad's posh Koshar Market on January 4, 2011.
The review petition was dismissed by a three-judge panel headed by Justice Asif Saeed Khosa.
"Mumtaz Qadri has confessed to the killing at all stages and was arrested from the crime scene," the court said.
"It is our responsibility to safeguard the law and stand by our oaths," Justice Khosa said.
The punishment was upheld by the Islamabad High Court and later also confirmed by the Supreme Court this year.
Qadri had filed review of the case with the Supreme Court which it rejected.
The court said that Qadri's lawyers had failed to "establish blasphemy" in the case, which was the major defence by the convict who had said that the governor had committed blasphemy and he was right to kill him under religious obligations.
Qadri threatened to commit suicide if he is not allowed to meet his family in a separate room in Rawalpindi's Adiala Jail last month.
Taseer while visiting Asia Bibi, a Christian woman sentenced to death for alleged blasphemy, had termed these laws as "black laws", which drew criticism from the extremists and right wing parties.
Blasphemy laws were introduced in Pakistan in mid-1980s during the time of military ruler Ziaul Haq and are allegedly used by people to settle personal scores.
Apart from assassination of Taseer, minister Shahbaz Bhatti, a Christian, was also killed in 2011 for demanding changes in the blasphemy laws.