Official results were yet to be declared but figures showed that Rajapaksa has already won 51.12 per cent of the votes, with Premadasa trailing with 42.92 per cent of the ballots, reports the Daily Mirror newspaper.
The official result will "hopefully" be announced by 4 p.m. on Sunday, the Election Commission Chairman Mahinda Deshapriya told the BBC.
Around 80 per cent of the nearly 16 million eligible Sri Lankans voted on Saturday in the election which was the first in the country since the April 21 Easter Sunday terror attacks that killed more than 250 people, and the third since the end of the country's decades-long civil war in 2009.
Incumbent President President Maithripala Sirisena was not on the ballot as he decided against running after coming under criticism following the April bombings which were claimed by the Islamic State terror group.
A record 35 candidates contested for the Presidency, but the main fight was confined between Rajapaksa and Premadasa.
Gotabaya is retired soldier who took over Sri Lanka's defence portfolio during the period when his older brother, Mahinda Rajapaksa was President (2005-2015) and also when Sri Lanka ended its war in 2009 with the Liberation Tigers of Tamil Eelam (LTTE).
On the other hand, Sajith Premadasa, the son of Ranasinghe Premadasa who served as the President from 1989 until he was assassinated in May 1993 by the LTTE, has pledged to fight for the Muslim and Tamil minorities.
The votes from the minority community had also played a major role in Sirisena's 2015 victory.
But the two candidates also promised something different on the international stage. Gotabya Rajapaksa said he planned to "restore relations" with Sri Lanka's top lender, China, if he wins the election, reports the BBC.
Sajith Premadasa, meanwhile, was seen as leaning more towards India and the US.
Saturday's percentage was a little less than the 2015 Presidential election when average voting percentage was 81.52 per cent out of which Sirisena won with 51.28 per cent with 6,217,162 votes while Mahinda Rajapaksa garnered 47.58 per cent with 5,768,090 votes.
( With inputs from IANS )