Modi was welcomed at the airport by Sri Lankan Prime Minister Ranil Wickremesinghe.
India will be giving an aid of $2.6 billion for the hospital.
He will also address the Indian origin Tamil community at Norwood Grounds. Renowned sand sculptor, Sudarshan Patnaik is in Colombo.
Celebrated sand artist Sudarsan Pattnaik will be making world's longest sand Buddha statue at a special Vesak zone near Sri Lankan Parliament.
The UN Vesak Day celebrations will be celebrated across Sri Lanka this week to commemorate the birth, enlightenment and passing away of Lord Buddha.
The commemorations will include an International Buddhist Conference, with the participation of over 400 delegates from more than 100 countries.
This will be his second visit to the country in two years showing the importance India attaches to the bilateral relationship.
As part of the celebrations, Modi will participate in a lamp lighting ceremony later on Thursday at the Gangaramaya temple in Colombo, one of the most important temples in Sri Lanka. Chief guest of the event is going to be PM Modi. Sri Lanka's hilly regions home Indian Tamil people who work in tea plantains.
The visit and the agenda are mainly to re-emphasise the traditional connect between India and Sri Lanka, particularly in the context of Buddhism, which is a shared heritage. On Indo-Sri Lanka economic and technology cooperative agreement, Mr Panda said, four rounds of discussions have been completed and it is expected to be finalised by the end of this year.
Sri Lanka refused permission for a Chinese submarine to dock at Colombo next week after a similar visit in 2014 angered India, a top defense official said Thursday.
Prime Minister Narendra Modi and Sri Lankan President Maithripala Srisena had a meeting here tonight during which the two leaders are understood to have reviewed the status of the bilateral relations.