President Maithripala Sirisena's new Cabinet was also sworn in and Rajapaksa was named the new minister of finance and economic affairs.
PM Modi is due in Colombo on Friday.
Sri Lanka has refused to cooperate with a United Nations investigation into alleged war crimes during the final phase of the country's civil war, saying it will not subject itself to the jurisdiction of the top rights body.
The two brothers led a decisive campaign that helped end the island nation's three decade long civil war against the Liberation Tigers of Tamil Eelam.
The docking of two Chinese submarines at the Colombo harbour in 2014 had angered India, which said it undermined its security interests.
Reaching out to President-elect of Sri Lanka Maithripala Sirisena, Prime Minister Narendra Modi on Friday congratulated him on his electoral victory and said he looked forward to working with him to take the bilateral ties to a new level.
The UN Human Rights Council in Geneva on Tuesday adopted a resolution against Sri Lanka's rights record, in a setback to Colombo, which made determined efforts to garner international support ahead of the voting.
President will lead a five-member delegation to the memorial service.
'It is up to New Delhi to take quick advantage of the turn of events in Sri Lanka. Otherwise, Beijing's economic clout and the deep roots it has grown in the island nation may well tempt the new President to play the India versus China game,' says Nitin A Gokhale.
Prime Minister Narendra Modi and leaders of other South Asian Association for Regional Cooperation countries will meet in Kathmandu on Wednesday with an aim to revitalise the regional grouping and make it a major platform to fuel economic growth through liberalised trade and combat challenges of terrorism and climate change effectively.
The Prime Minister's Office has convened a meeting tomorrow to explore a long-term solution to the contentious fishermen issue between India and Sri Lanka.
According to observers, with pro-China Rajapaksa winning the election, the result will have a bearing on India's presence in the Indian Ocean region where Beijing is increasingly making inroads.
'Gotabaya will expect India to observe the red line.' 'He even dispensed with any gesture welcoming India as an interlocutor on the Tamil issue.' points out Ambassador M K Bhadrakumar.
Sirisena's sacking of Wickremesinghe was the culmination of an year of bitter relations between them on several policy matters. The president has been critical of the prime minister and his policies, especially on economy and security.
'Rajapaksa's victory poses a serious foreign policy challenge for the Modi government,' notes Ambassador M K Bhadrakumar.
'If Ranil Wickremesinghe starts repressing and suppressing the protesters who represent the people, that will pose a danger for him to continue in office.'
Kanyakumari is the tip of India and will convey the symbol that from the tip of India, the Congress is on its way up.
Sri Lankans on Thursday voted in large numbers in the bitterly contested presidential election in which incumbent Mahinda Rajapaksa is seeking a record third term against his friend-turned-foe Maithripala Sirisena, with an unusually high voter turnout in Tamil and Muslim areas.
External Affairs Minister Sushma Swaraj arrived in Colombo on Friday on a two-day trip to set the stage for Prime Minister Narendra Modi's visit to Sri Lanka next week, the first bilateral visit to the country by an Indian premier in over 25 years.
Sri Lanka's new president will embark on a 4-day visit to February 15.
Lanka is witnessing a political crisis since October 26 when President Sirisena sacked Wickeremesinghe and replaced him with Rajapaksa.
'No one in Sri Lanka could afford to stay at home, everyone came onto the street.'
Sri Lankan President Maithripala Sirisena on Friday dissolved the parliament, paving the way for fresh parliamentary elections in mid August, eight months ahead of the schedule.
'Putting tanks on the Ladakh border is not enough to combat China, what is needed to ensure resilience against any cyber-attacks or attacks in outer space or China flexing its economic muscle, as it did with Australia.'
Dealing with the Sirisena government in Sri Lanka, says G Ganapathy Subramaniam, is a lot easier for India than engaging with the Rajapaksa regime.
On the lingering Tamil issue, Modi said he was confident that the Sri Lankan government will carry forward the reconciliation process and fulfil the aspirations of the Tamil community.
Rajapaksa is the first president to be sworn in outside Colombo.
Prime Minister Narendra Modi on Wednesday arrived in Frankfurt en route to New Delhi after concluding his visit to the US where he met President Barack Obama and agreed to make joint efforts to dismantle terrorist safe havens besides stepping up cooperation in defence, energy, economy and space.
Ahead of Prime Minister Narendra Modi's visit to the United States, External Affairs Minister Sushma Swaraj held bilateral meetings with foreign ministers of seven countries, including the United Kingdom, on the sidelines of the 69th session of the United Nations General Assembly on Wednesday.
Sri Lankan President Mahindra Rajapaksa on Tuesday told the United Nations General Assembly that Colombo is concerned over the growing trend of international interference in the internal affairs of developing countries in the guise of concern for security and human rights.
Sri Lanka on Thursday freed 33 Indian fishermen arrested for allegedly poaching in the country's waters, days after President Mahinda Rajapaksa ordered their release as a goodwill gesture.
LTTE leaders has been barred by SL court to travel out of the country
With some countries like Britain and Canada seeking to bring alleged human rights violations in the Sri Lankan civil war against the Liberation Tigers of Tamil Eelam under the scanner during the Commonwealth Heads of Government Meeting summit, President Mahinda Rajapaksa on Friday asked member nations not to turn the Commonwealth into a "punitive and judgmental" body and desist from introducing bilateral agendas.
India has dismissed reports that the Colombo station chief of the Research and Analysis Wing had been expelled in the run up to this month's Sri Lankan presidential election and maintained that he has moved out after completion of his three-year tenure.
Five fishermen from Tamil Nadu, who were sentenced to death in Sri Lanka for alleged drug trafficking but set free after President Mahinda Rajapaksa pardoned them, arrived in Chennai on Friday.
As many as 16,000 Sri Lankans -- who disappeared during the war against the Liberation Tigers of Tamil Eelam -- will be issued certificates of absence instead of death certificates, head of a probe panel said on Wednesday.
What comes as a relief to five families, Sri Lankan President Mahinda Rajapaksa has agreed to pardon and release the five Tamil fishermen serving a death sentence for drug smuggling in the island nation.
Protests rocked different parts of Tamil Nadu for the second day on Friday against the capital punishment awarded by a Sri Lankan court to five Indian fishermen for alleged drug trafficking.
At least 10 persons were killed and up to 300 missing on Wednesday after a massive landslide triggered by monsoon rains struck central Sri Lanka, forcing authorities to deploy the army to conduct rescue operations.
"Sri Lanka regrets that the prevailing environment in the region is not conducive for holding the 19th SAARC Summit in Islamabad," the foreign ministry said in a statement.