The Union Cabinet approved amending the Act after the HRD Ministry took a decision to set up a central university in Motihari in addition to the one already proposed in Gaya.
This is only the second exception made by the Union government for setting up two central universities in a particular state, the first being Jammu and Kashmir.
The Act had a provision for setting two central universities in Jammu and Kashmir as a special case.
The government's decision for setting up a central university in Motihari had put an end a prolonged slugfest over the issue.
Bihar Chief Minister Nitish Kumar and other political parties had been insisting that the central university should be established in Motihari to end regional disparities, leading to a slugfest for months.
The Bihar Assembly had even passed a resolution to demand the university in Motihari.
The Ministry has, however, said there would be no additional allocation for Bihar and the Rs 240 crore meant for the state for the central university would now be divided among the two varsities.