Former Presidents Maumoon Abdul Gayoom, Mohamed Nasheed and Dr. Mohamed Waheed attended the ceremony, while Solih's predecessor Abdulla Yameen chose to boycott it. Solih's party has criticized China's activities in the country, and is expected to review major projects.
In a Facebook post before his departure, Modi offered congratulations and said, "I will convey to the new Maldivian government of Mr Solih the desire of my government to work closely for the realisation of developmental priorities, especially in areas of infrastructure, healthcare, connectivity and human resource development".
MDP leader and former president Mohamed Nasheed has vowed his party would reduce reliance on China and renegotiate loans taken from Beijing.
Solih's swearing-in ceremony took place at the Galolhu National Stadium on Saturday evening during a Parliament sitting.
Solih, 54, emerged as a common candidate for the opposition that united to oust strongman leader Abdulla Yameen in a September election.
Modi was the senior-most foreign leader to attend the ceremony in the Indian Ocean archipelago nation that went through vast political turmoil under former President Abdulla Yameen. "We in India strongly desire to see a stable, democratic, prosperous and peaceful Republic of Maldives".
India has been the country's traditional main ally but Yameen became close to China and the Maldives saw its foreign debt balloon to more than $1.2 billion during his five years in power.
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Counties have until noon on Sunday to file their official results, but it appears the gap is too far for Nelson to close. But Gillum issued only a brief statement saying, "It is not over until every legally cast vote is counted".
"Recent elections in the Maldives represent the collective aspirations of the people for democracy, rule of law and a prosperous future".
Former President Yameen was seen as anti-India and pro-China while new President Solih is perceived to be pro-India.
India's Prime Minister Narendra Modi was the most high-profile guest at the inauguration and the pair pledged to work together on the problems faced by the nation of small islands and atolls.
Ibrahim Mohamed Solih will take oaths as the new President tomorrow at a ceremony which will also be attended by Indian Prime Minister Narendra Modi.
On the economic front, Solih briefed PM Modi on the dire economic situation in the country, and the two discussed ways in which India can continue the development partnership. An ongoing constitutional crisis in Sri Lanka is also said to be linked to India and China's tussle over expansion of their influence in the Indian Ocean region.
According to the joint statement, the Maldives Minister of Foreign Affairs will make an official visit to India on November 26 to hold further discussions and to prepare for the forthcoming state visit of Solih to India.