Mr Hague, who had called for the restrictions on weapons to be relaxed, said the EU's decision was the "right" one but added that "no immediate decision" would be made on sending arms to rebels.
After more than 12 hours of talks in Brussels last night, the Foreign Secretary insisted that the Government's focus remained on a "political transition" in Syria.
– Foreign Secretary William Hague
Tonight EU nations agreed to bring the arms embargo on the Syrian opposition to an end. This was the outcome that the United Kingdom wanted.
It was a difficult decision for some countries, but it was necessary and right to reinforce international efforts to reach a diplomatic solution to the conflict in Syria.
It was important for Europe to send a clear signal to the Assad regime that it has to negotiate seriously, and that all options remain on the table if it refuses to do so. Tonight EU nations have done just that.
The other elements of EU sanctions on the Assad regime will be retained. EU nations also agreed a common framework for those member states who, in the future, may decide to supply military equipment to the Syrian National Coalition.
These agreed safeguards would ensure that any such equipment would only be supplied to the National Coalition, for the protection of civilians.
This does not mean that we have made any decision as the United Kingdom to send arms to the National Coalition, but we now have the flexibility to respond in the future if the situation continues to deteriorate and if the Assad regime refuses to negotiate.
Thousands of lives are at stake in Syria. Our focus remains on efforts to secure a successful outcome at the forthcoming Geneva conference, and a political transition that ends the conflict, allows refugees to return to their homes, and prevents further radicalisation in Syria.
The Foreign Affairs Council declaration issued after the meeting said member states such as the UK who wished to supply arms would have to ensure "adequate safeguards against misuse" including "relevant information concerning the end-user and final destination of the delivery".
No arms shipments can take place yet but the Council will review its position before August 1.
But former Liberal Democrat leader Sir Menzies Campbell, a member of the Commons Foreign Affairs Committee, said the decision was "gesture politics on a grand scale" that "we may live to regret".
– Sir Menzies Campbell, a member of the Commons Foreign Affairs Committee
The UK has helped to divide the EU, no matter what is being claimed to the contrary.
Sooner or later weapons will be sent to the Syrian opponents of Assad with no prospect that he will be persuaded to change his stance or any guarantee that such weapons will not fall into the hands of extremists who care nothing for democracy or human rights.