During the meeting that lasted for about an hour, Prime Minister Modi invited the Bhutanese King and his wife Jetsun Pema to visit India.
Sources described the meeting between the two as "very good".After the meeting, both the King and Prime Minister Modi posed for photographers while shaking hands. They were then joined by the King's wife Pema and external affairs minister Sushma Swaraj for a photograph.
Before the meeting when Prime Minister Modi arrived at the palace, he was given a warm, ceremonial welcome with a traditional dance.
He was also presented with a guard of honour at the palace and the national anthems of the two countries were played. Just before Prime Minister Modi's arrival at the palace, there was heavy rainfall which raised speculation whether the guard of honour conducted in an open court could be affected.
However, the rain stopped just in time for the ceremony to take place in grand style. Modi, on his first foreign trip as the Prime Minister, is accompanied by Swaraj, National Security Advisor Ajit Doval and Foreign Secretary Sujatha Singh.
Before embarking on the two-day visit, Modi said Bhutan was a "natural choice" as his first foreign destination because of the "unique and special relationship".
The fact that the Prime Minister chose Bhutan as his first foreign destination assumes significance since China has lately intensified efforts to woo it and establish full- fledged diplomatic ties with Thimphu.
In his pre-departure statement, Modi said relations with Bhutan will be a key foreign policy priority of his government.
"I am looking forward to my first-ever visit to Bhutan and to nurturing and further strengthening India's special relations with Bhutan," said Modi.
India's assistance package to Bhutan includes Rs 4,500 crore for the country's 11th Five Year Plan from 2013-18 and covers areas from infrastructure and information and communication technology to health, agriculture, human resource development and tourism.
Bilateral trade amounted to Rs 6,830 crore in 2012 and education, media and tourism sectors hold good potential for enhanced cooperation in future.