On his first visit to the country since taking charge last month, Tshering was received by Minister of State for Finance Shiv Pratap Shukla.
Later in the evening, Foreign Secretary Vijay Gokhale called on the Bhutanese prime minister and discussed key issues of mutual interest.
He will be given a ceremonial reception on Friday and will hold talks with Prime Minister Modi the same day.
Sources said a host of issues, including Bhutan's five-year development plan, were likely to be discussed during the visit.
The Ministry of External Affairs had earlier said that all aspects of bilateral relations, including high-level exchanges, people-to-people ties, economic development and hydropower cooperation were expected to be discussed between the two sides.
The upcoming visit of Tshering will provide an opportunity to the two sides to review the progress in the multi-faceted partnership, and discuss ways and means to expand the enduring ties of friendship and cooperation, the MEA had said.
Tshering's visit comes a month after Foreign Secretary Gokhale's official trip to Bhutan.