"Sri Lanka People's Front has secured a resounding victory according to official results released so far," Gotabaya Rajapaksa said in a Twitter message. "It is by belief that that the expectation to have a Parliament that will enable the implementation of my 'vision for prosperity' policy will be reality tomorrow."
Critics fear the siblings - renowned for their crushing of Tamil separatist rebels to end a decades-old conflict in 2009 - want to end presidential term limits, bring the judiciary and police under their direct control, and extend their dynastic power to a new generation.
Sri Lanka's opposition has accused the government of corruption, censorship and intimidation.
"The handling of coronavirus crisis by President Gotabaya Rajapaksa has invoked a lot of confidence in the people in contrast with the shambles the last government made following the Easter bombing attack last year."
The Indian Ocean Island has largely contained the spread of the novel coronavirus with 2,839 confirmed cases, including 11 deaths.
However, analysts say any attempt by Gotabaya Rajapaksa to push for changes that will strengthen presidential power at the expense of those of the prime minister may trigger sibling rivalry.
Gotabaya was elected president last November after projecting himself as the only leader who could secure the country after bombings of churches and hotels on Easter Sunday killed 269 people in 2019.
Since being elected, he has said he had to function under many restrictions because of constitutional changes in 2015 that strengthened Parliament and the prime minister and put independent commissions in charge of judiciary appointments, police, public services and the conduct of elections
Mahinda Rajapaksa is unlikely to cede any of his powers that might shrink his influence as he works on promoting his son, Namal, as his heir. Namal and three other members of the Rajapaksa family contested the election and are likely to control key functions in the new administration.
A man hangs newspapers carrying headlines about the victory of Mahinda Rajapaksa's Sri Lanka People's Front party in the country's parliamentary election in Colombo
Former Prime Minister Ranil Wickremesinghe lost his constituency, and his party, which had 106 seats in the outgoing parliament, was reduced to just one seat.
A breakaway faction from Wickremesinghe's party headed by the son of assassinated President Ranasinghe Premadasa, Sajith, got 20 percent of the vote and was a distant second with 54 seats.
The moderate Tamil National Alliance (TNA) which had 16 seats in the outgoing parliament, also suffered badly and was left with just 10 seats in the new assembly, which is due to sit on August 20.
A total of 196 seats in the 225-member house were decided on district proportional representation while the remaining 29 were decided on the basis of votes polled nationwide.
The election was originally scheduled for April, but it was twice postponed because of the COVID-19 pandemic.