Hague said on Tuesday there had been a "marked change" for the better in relations between the two sides since President Hassan Rouhani was elected in June.
"Both our countries will now appoint a non-resident charge d'affaires tasked with implementing the building of relations, including interim steps on the way towards (the) eventual reopening of both our embassies," Hague told parliament.
"It is clear that the new president and ministers in Iran are presenting themselves and their country in a much more positive way. We must test the Iranian government's sincerity to the full."
The announcement reflects a significant thawing in Iran's relations with the West which imposed tough economic sanctions on Tehran after the embassy closure. It may raise hopes of a breakthrough in talks with world powers about its nuclear program in Geneva next week.
Britain's two diplomatic compounds in Tehran were overrun on an afternoon in November 2011, after a rally against British sanctions escalated into violence and protesters scaled the walls.
Although the protesters withdrew after a rampage, Britain immediately withdrew all staff, closed the embassy, and ejected Iranian diplomats from London.
NTJ/BA