Sarkisian had an unassailable lead with 844,088 votes, giving him 52.7 per cent of the votes counted, according to official results shown on Armenian public television.
Analysts had predicted Sarksian would struggle to win the more than 50 per cent needed to avoid a second round.
But the results, from 97.5 per cent of the ballots counted, looked set to give Sarkisian outright victory and let him avoid a runoff with his closest rival, Levon Ter-Petrosyan, opposition leader and former president.
Ter-Petrosyan had 344,619, or 21.5 per cent, of votes counted, as calculated by Reuters news agency.
In the Caucasus mountains, land-locked Armenia lies between Turkey and Azerbaijan in an important transit region for oil exports from the Caspian Sea to world markets.
Sarkisian had been seen by many as improving living standards and facilitating economic growth in the country, but Armenia's poverty level still remains high.
One of the biggest tasks facing the new president will be the ongoing conflict with neighbouring Azerbaijan over the territory of Nagorno-Karabakh.
On Tuesday, Sarkisian's campaign team said it was waiting for definitive official results before making a statement and that the priority was for a free and fair election.
But an opposition aide said Ter-Petrosyan, Armenia's first president after it won independence from the Soviet Union, was the real winner, and complained of violations including ballot-stuffing, kidnapping and the beating of supporters.
Sarkisian's two main rivals, Ter-Petrosyan and Artur Baghdasarian, a former parliamentary speaker, boosted the prime minister's chances of winning the election by failing to unite ahead of the vote.
Opponents of Sarkisian, however, accuse his camp of making unfair use of state resources to promote his candidacy, a charge the prime minister has denied.
Ter-Petrosyan's party announced that a rally would take place in the capital, Yerevan, on Wednesday, to protest that elections had been marred by serious violations.
"Very dirty things are happening," he said after voting.
Arman Musinian, his campaign spokesman, said that dozens of Ter-Petrosyan's supporters had been beaten on Tuesday across the country.
He also claimed that ballot stuffing, multiple voting and voter intimidation had been widespread.
"It's already clear that this is not an election. This is an attempt by the authorities to seize power," Musinian said.
About 600 foreign observers have been monitoring the vote, and election observers from the Organisation for Security and Co-operation in Europe will give their verdict on the vote on Wednesday.
Voter turnout was 69.25 per cent, the Central Election Commission reported.
Previous elections in Armenia have been followed by days of opposition protests alleging ballot fraud.