It is vital that the Egyptian elections lead to "legitimate, accountable and democratic governance", William Hague has said.
The Foreign Secretary said he welcomed the peaceful conduct of the polls, but the country faced a "critical moment".
It is just over a year since a violent revolution saw Hosni Mubarak being forced to step down from the presidency.
The Muslim Brotherhood's Freedom and Justice Party says its chairman, Mohammed Mursi, received 52% of the vote, while former prime minister Ahmed Shafiq said he had 48%.
The official results are not due to be announced until Thursday but the Islamist movement, which will most likely be leading the country, is set to protest against a decree the ruling military generals have put in place.
The decree ordered the immediate dissolution of parliament after the Supreme Constitutional Court ruled that the law governing the first elections were unconstitutional as party members had been allowed to contest seats reserved for independents.
The second decree amended the March 2011 constitutional declarations by giving generals complete control over legislation and military affairs until fresh parliamentary elections are held.
Mr Hague said: "I welcome the peaceful conduct of the second and final round of Egypt's presidential elections. This is a critical moment in the process towards democratic civilian-led government in Egypt. It is important that whoever wins has done so through a credible, free and fair process, which fully reflects the will of the Egyptian people. I look forward to the announcement of the results due on Thursday.
"It is vital that the transition leads to legitimate, accountable and democratic governance, underpinned by strong and accountable institutions. We were concerned by recent announcements of the dissolution of parliament and the reintroduction of powers of arrest and detention for the military. The process of drafting a new, inclusive constitution and the holding of new parliamentary elections should be taken forward as soon as possible.
"The UK will continue to support the people of Egypt in their aspirations for greater economic opportunities, political participation, freedom and rights, and to that end work with the Egyptian leadership elected by the people."