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Mr Hague said the "circumstances were right" following an improvement in bilateral relations in recent months, BBC said.
Full diplomatic relations with Iran were suspended after attacks on the British embassy in Iran in 2011.
The election of a new Iranian president and agreement on how to deal with Iran's nuclear programme has led to increased contacts in 2014.
The move comes as Iraqi forces are engaged in heavy clashes with Sunni Islamist militants across the country and amid reports that Iran is providing military assistance to its historic rival.
The US is deploying up to 275 military personnel to protect staff at its huge embassy in Iraq.
In a written statement, Mr Hague said the UK embassy will re-open "as soon as practical arrangements are made" as a sign of "increasing confidence" in the state of relations between the two countries.
"There has never been any doubt in my mind that we should have an embassy in Tehran if the circumstances allowed," he said.
"Iran is an important country in a volatile region, and maintaining embassies around the world, even under difficult conditions, is a central pillar of the UK's global diplomatic approach."
The foreign secretary, who will give further details to MPs at 11:30 BST, said he had sought assurances that British diplomatic staff would be safe and would be able to carry out their work "without hindrance".