However, none of the 27 European member states intends to send any arms to the rebels in the coming months, for fear of endangering a US-Russia peace initiative for Syria.
After a gruelling 12 hours of talks, British Foreign Secretary William Hague announced the deal to lift the arms embargo against the rebels, while maintaining the remainder of a far-reaching two-year package of sanctions against Syrian President Bashar al-Assad's regime.
Without such a deal, the entire set of sanctions, including an assets freeze on Assad and his cronies, and restrictions on trade in oil and financial transactions, would have lapsed at midnight on Friday.
But the agreement reached by EU foreign ministers in Brussels failed to come underpinned by a tight range of safeguards demanded for both ethical and political reasons by opponents of the long-running Franco-British push to arm Syria's rebels.
"It was not possible to find a compromise with France and Britain," said Austrian Foreign Michael Spindelegger, a longtime outspoken opponent of the move.
Austria, Sweden, Finland and the Czech Republic were reticent about pouring more arms into a conflict that has already cost some 94,000 lives.
To send arms is "against the principles" of Europe which is a "community of peace", said Spindelegger.
A French official in Paris stressed that "this is a theoretical lifting of the embargo. In concrete terms, there will be no decision on any deliveries before August 1".
Such a delay will allow for the planned US-Russia sponsored international peace conference on Syria, which it is hoped both the Assad regime and opposition figures will attend, to take place in Geneva in June.
The deal made in Brussels leaves the decision to supply arms to the rebels up to each nation. Ministers nonetheless vowed to stick to safeguards against misuse and to respect EU rules on arms exports.
Hague stressed that Britain, while championing the move, had "no immediate" plans to supply weapons to the rebels fighting Assad.
"None of the member states have the intention of actually providing arms at this stage," said Frans Timmermans, the Dutch minister who tried to steer a compromise.
"Member states will have to decide for themselves in the future whether they will provide groups with arms in that region."
But a written vow to respect a joint moratorium on supplying arms until after the planned peace conference in Geneva next month was eliminated in the final deal.
In Istanbul, Syria's opposition Coalition had urged EU foreign ministers to lift the embargo.
"It's the moment of truth that we've been waiting for for months," said spokesman Khaled al-Saleh.
Hague said it had been a "difficult" decision for EU partners who believe delivering arms would serve only to fuel the conflict.
"I think it is the right decision," he added. "It will support political progress on Syria and our attempts to bring together a Geneva (peace) conference."
Hague said Britain saw only a political solution and a diplomatically supported solution for Syria but that Monday's ground-breaking decision "sends a very strong message from Europe to the Assad regime of what we think of the continued brutality and murder and criminality of this regime".
French Foreign Minister Laurent Fabius left the talks before the finish to meet in Paris with his Russian and US counterparts, Sergei Lavrov and John Kerry, over efforts to convene the Syria peace conference in Geneva.
According to a document obtained by AFP, a compromise favoured by most nations would have formally postponed the actual delivery of arms until a fresh political decision by all EU members by August 1 "in light of the developments related to the US-Russia initiative".
"Quite a lot of arms are already going to the wrong hands," said Timmermans. "The parties to the conflict don't have a shortage of arms, frankly."
EU diplomats said Britain had refused to agree to put the decision to the EU a second time by August 1. It wanted the deal to be implemented automatically after a set period.