The bill, which prescribed a five-year jail term for lecturers and educators convicted of sexual harassment of their male or female students had last year been rejected by the lower house when it was sent for concurrence.
It also recommended expulsion or suspension for students whose claims of being serially abused by lecturers or educators are found to be false by any competent court.
Another provision of the bill is a fine of N5 million in the event that the accused person is convicted by a competent court of law.
The BBC documentary exposed two lecturers of the University of Lagos, and two lecturers of the University of Ghana as engaging in sexual harassment of students.
Both institutions have distanced themselves from the claims and suspended the lecturers involved, who have denied the allegations.
If the bill is passed, it would also make it illegal for lecturers to make sexual advances towards their students.