UEFA said the convention would include a better exchange of intelligence between police forces to warn countries hosting matches of potential troublemakers.
The Euro 2016 tournament being played in France has seen a return of football hooliganism which had been largely absent from recent international competitions.
The worst incidents happened in Marseille before and after the match between England and Russia where clashes lasted several days.
“I’m sure that in the future we can use the intelligence of various police forces,” said Michael van Praag, head of UEFA’s Stadia and Security committee.
“That has not been working 100 per cent until now and this is the reason why we have this convention.
“I am sure in the future when this exchange of information between countries and police forces will go on, problems like the one we had in Marseille and in many competitions in Europe will belong in the past,” the Dutchman told reporters.
Van Praag said that “we can and must do more” to avert hooliganism and described the Council of Europe convention as a “significant step” forward.
However, he rejected a suggestion that tournament organisers should change venues and kickoff times for matches which were considered high risk.
“The authorities were very well prepared to organise this match but nobody expected this (violence) to happen on such a level,” he said.
“You cannot expect the tournament organisation to beforehand change kickoff times, or beforehand change the venues.
“We knew for months in advance that this match had to be played in Marseille and there were no signals whatsoever that the game would be disturbed in the way it was.”
France, Bulgaria, Georgia, Greece, Lithuania, Moldova, Monaco, Montenegro, Netherlands, Portugal, Russia, Switzerland, Macedonia and Ukraine were the countries who signed.
Council of Europe Secretary General Thorbjorn Jagland said he expected more countries to sign up.
“This is the opening day for signing the convention and it is extraordinary that so many signed on the first day, it’s nearly a record. We expect that many will follow suit,” he said.