The centre, known as Kompleks Nashrul Quran, is built on a 6.15ha land located at Precinct 14 in Putrajaya, AsiaOne reported.
Nashrul Quran is Arabic for Quran distribution.
The project costs RM60mil (S$21 million), which includes the building, and printing and binding machines.
It was announced by Najib when tabling the 2015 Budget last October.
In his speech yesterday, Najib said the center was expected to print up to three million copies of the Quran a year to be distributed worldwide.
"The centre will become a new landmark of Putrajaya and Malaysia.
"The initiative also supplements the Malaysian Shariah Index, the first ever shariah index in the world which was launched earlier this year," he said.
The shariah index will serve as a benchmark to determine if the country is fulfilling the objectives of Islamic principles.
The Malaysian Shariah Index will gauge objectively and scientifically Malaysia's commitment in achieving the five aspects of the Maqasid Shariah (objective of Islamic principles).