"This is an historic moment for Afghanistan and its people," Hague said in a statement.
"It is a great achievement for the Afghan people that so many voters, men and women, young and old, have turned out in such large numbers, despite threats of violence, to have their say in the country's future."
Afghans celebrated a largely peaceful election on Saturday, as turnout exceeded predictions despite Taliban threats to disrupt the vote to choose President Hamid Karzai's successor.
The second-largest contributor of international forces in Afghanistan after the United States, Britain has 5,200 troops in the country, based at Camp Bastion in Helmand.
Britain handed over command of the southern province to US forces on Tuesday as part of the withdrawal of combat troops, to be completed by the end of this year.
Some 448 British troops -- the last on March 5 -- have lost their lives since the start of operations in October 2001.