Several witnesses said the student, named Andrew Cate Carr, was walking along a wall above the Tiber river near Rome's Trastevere district, when he lost his balance and plummeted to the ground at around 2 a.m. on Tuesday.
"We saw someone walking and jumping on the wall. They were swaying around and then suddenly they fell," a witness told La Repubblica daily.
Carr, a student at Rome's John Cabot University, was earlier drinking with friends in bars in the nearby Campo de' Fiori square and in Trastevere, police said.
Carr is not the first person to have fallen to his death beside the Tiber.
"This is the fifth fatal incident along the Tiber in the past five years, which proves that the city council needs to implement security measures to stop more people falling and being killed," said consumer watchdog Codacons president Carlo Rienzi.
He urged safety nets to be put up to break people's falls and security cameras to allow police to monitor and intervene immediately in "potentially dangerous situations".