Timi Ariyo spoke out after a video about him containing abusive singing and monkey noises was sent on Snapchat.
Tami Sotire said she had been scared to report her abusers for fear the group would "become more angry".
A University of Bristol spokesman described their experiences as "extremely distressing".
The video, posted in December, showed a group of white men singing an abusive song about Mr Ariyo.
The pair, from Essex, said their abusers were mainly from their old school back home, but also included a fellow university student.
Both students met with Pro Vice-Chancellor, Prof Nick Lieven, and showed him screen shots of social media and other evidence of the bullying which they have suffered.
"Timi and Tami's experiences are extremely distressing. We are taking immediate action under our disciplinary procedures in relation to the student at our university, and will be looking to coordinate with the other universities involved," a spokesman said.
"We are already reviewing our own processes and communications so that we can make it easier for students to report these kinds of issues in the future."
A university says it is taking "immediate action" after two black students were subjected to months of "malicious" online racial abuse.