Francesco Ianari, 26, and Mauro Pinnelli, 25, were arrested within hours of the incident at the Drunken Ship pub on the Campo de' Fiori in central Rome last Thursday.
Several Spurs fans were badly injured, with 25-year-old Ashley Mills still receiving treatment in hospital after suffering a stab wound to his thigh.
A statement on Rome police headquarters' official website read: "Agents of Rome police have informed two Roma fans in our custody that they are banned from accessing sporting events for the next five years.
"Francesco Ianari and Mauro Pinnelli were arrested on November 22 for aggression towards some British fans of Tottenham on the Campo de' Fiori after being identified by police a few hours later.
"On that occasion, a group of people, most of them with their faces covered, entered the Drunken Ship pub and attacked some English supporters. Some of them were injured in the raid, one injury being particular serious.
"Thanks to testimonies and images taken from some cameras in the area, the commissariat of Trevi was able to identify two of the participants.
"The superintendent of Roma, Fulvio Della Rocca, has considered the circumstances of the facts and issued the two fans with (the ban) for a duration of five years."
Ianari and Pinnelli remain in custody in Regina Coeli prison after having initial charges of attempted murder downgraded to aggravated wounding during a court appearance on Monday.