Mr Hague said the sanctions agreed on Monday in Luxembourg, which include travel bans and asset freezes against senior members of the regime, meant those who ordered the torture of civilians would be treated "harshly" once a new government was in power.
Mr Hague said: "No country should shut its eyes to the horrors we are witnessing. History and the Syrian people will judge them harshly if they do. These new sanctions give a clear warning to those close to the regime that if they back Assad and commit acts of violence and torture against civilians, the international community will hold them accountable."
Meanwhile, Immigration Minister Mark Harper said in a written ministerial statement to parliament that Syrians currently in the UK will be able to apply to extend their stay without having to return home first.
The EU's Foreign Affairs Council also agreed more sanctions against Iran, which are aimed at making it harder for President Mahmoud Ahmadinejad to finance his nuclear programme. The measures include a ban on transactions with the country's banks, while export credit insurance will also be prohibited.
Foreign ministers also agreed to ban the export of naval equipment and raw materials such as graphite to Iran in an attempt to make it harder for the regime to develop a nuclear arsenal. The EU already has an oil embargo in place but it has now prohibited the trade of natural gas.
Mr Hague said Iran now faced a "substantial" set of sanctions as it continued to defy the international community. He said the country's uranium enrichment programme was on a scale that meant there was "no plausible civilian justification".
"The EU's message today is clear: Iran should not underestimate our resolve," he said. "The choices being made by Iran's leaders are already having a profound impact.
"Today we have taken steps to prohibit financial transactions with Iranian banks, to intensify restrictions in the energy sector and to limit some areas of trade, in order to choke off revenue that Iran is using for its nuclear programme, prevent it from accessing materials for the programme, and prevent it from circumventing existing sanctions."