Seven people were injured, one with a knife wound, in the attack early Thursday at a pub in Campo de' Fiori square.
Italian news reports, quoting unidentified witnesses, said the hooligans shouted "Jew" during the attack. Tottenham is known for having a large Jewish fan base from north London.
The stabbing victim, Ashley Mills, remained in reserved condition on Friday after his femoral artery was gashed on his right thigh, according to a statement from Rome's San Camillo Hospital.
Police said that after investigations of 15 people and searches of homes, officers arrested Francesco Ianari, 26, and Mauro Pinnelli, 25. Police identified them as fans of Roma, Lazio's crosstown rivals.
Police said they were charged with causing a fight, causing injury and attempted homicide; one of the two also was charged with drug possession. They are due to appear before a judge on Saturday.
Lazio fans were initially suspected but the team denied its supporters were involved. Police said around 50 people rampaged through "The Drunken Ship" pub, which was badly damaged.
Ronald Lauder, the World Jewish Congress president, called on UEFA to take strong action against Lazio if it fails to crack down on racist outbursts by fans.
Already, UEFA is waiting to receive a report from the English Football Association into alleged anti-Semitic chants directed by Lazio fans at Tottenham during Thursday's match, which finished 0-0. UEFA fined Lazio €40,000 ($51,600) for its fans' racist behaviour when the teams played in London in September.
Italian football federation president Giancarlo Abete apologized on Friday to Tottenham, its fans and the families of those injured in a letter to his British counterpart, David Bernstein. Abete pledged to follow the investigation personally.
"Unfortunately once again, football has been the occasion for a group of delinquents to vent their racist and anti-Semitic rage, given that this was undoubtedly the motive of an assault that damaged Italian football's image and doesn't correspond with Rome's tradition of hospitality," Abete wrote.
Despite the damage inflicted, not all Tottenham supporters seemed surprised by the assault. Four men, eating breakfast on Friday at a cafe just meters from the trashed bar, said the attack wasn't nearly as bad as it had been portrayed. One man, nursing a bandaged head, black eye and cast on his right leg, said such violence was par for the course with Tottenham and downplayed the anti-Semitic nature of the attack. They declined to give their names, saying they didn't want any publicity.