Vincent (Vinny) Wall from Colligan, Dungarvan, was returning to his hotel in the early hours of Saturday with his friend, David McGrath, 25, when he apparently fell into the river in the Italian capital.
He was in a group of up to 40 people who travelled to Rome on Friday to celebrate the wedding of his childhood friend Johnny Kiely.
The wedding was cancelled following the tragedy.
The 27-year-old dairy farmer fell over the Ponte Mazzini Bridge overlooking the river and was swept away in the fast-flowing waters, swollen by heavy rains.
A member of the local Coast Guard threw Mr Wall a lifebuoy, but he failed to grasp it.
Witnesses said he was seen minutes later underneath the Sisto Bridge before he sank beneath the surface.
Dr Tom Higgins, mayor of Co Waterford, said: “The whole area is in deep sadness at the death of Vincent Wall. The community around the Dungarvan area and Colligan are numbed by this tragedy.”
Mr Wall was due to get married to his fiancee, named locally as Kathy, from Newry, Co Down, in Carlingford, in three weeks’ time.
Mr Wall’s fiancee, along with his devastated parents, Michael, a local dairy farmer, and Marian, a nurse at St Joseph’s Hospital in Dungarvan, travelled to Rome over the weekend. The Department of Foreign Affairs is providing consular assistance.
Italian authorities have continued to search the Tiber since the weekend. Heavy rain has seen the river rise to its highest in 40 years.
The mayor of Rome Gianni Alemanno declared a state of emergency last Thursday after storms caused seriously flooding to underpasses in parts of the city.