But analysts say he may struggle to win the more than the 50 per cent needed to avoid a second round.
Kocharian chose him as his successor after Sarkisian's Republican Party of Armenia swept parliamentary elections in May last year.
Both men are credited with ensuring relative stability.
Speaking to tens of thousands of supporters at a rally on Sunday, Sarkisian, 53, said his government was the only one voters could trust to maintain economic growth.
"I know there are many problems in our country - poverty, unemployment, corruption. We are the only political force that knows how to resolve these problems," he said.
Sarkisian's two main rivals - Levon Ter-Petrosian, former president, and Artur Baghdasarian, a former parliamentary speaker - boosted the prime minister's chances by failing to unite ahead of the vote.
Opponents accuse the Sarkisian camp of making unfair use of state resources to promote his candidacy, a charge the prime minister has denied.
Opposition candidates say they will call supporters to protest if they believe the vote is unfair, raising fears of post-election unrest.
Analysts predict Sarkisian will follow in Kocharian's footsteps if elected - pursuing close ties with Moscow and maintaining a hawkish stance with neighbouring Azerbaijan and Turkey.
The two countries have cut diplomatic ties and sealed their borders with Armenia over its support for Armenian separatists in Azerbaijan's rebel Nagorny-Karabakh region.
Ankara has also been angered by efforts by the Armenian capital, Yerevan, to have mass killings of Armenians by the Ottoman Empire in the first world war internationally recognised as genocide.
Pre-election polls showed Sarkisian hovering at about 50 per cent support, with Ter-Petrosian and Baghdasarian trailing with between 10 and 15 per cent.
Opposition candidates have questioned the polling companies' independence.
About 600 foreign observers are to monitor the vote and analysts say the government is keen to win international legitimacy for the result.
The Organisation for Security and Cooperation in Europe (OSCE) is to issue a report on the election on Wednesday.
Parliamentary elections last May were the first to be declared largely in accordance with international standards.