He will also meet President Ram Nath Kovind. Among others, Vice-President Venkaiah Naidu, External Affairs Minister Sushma Swaraj, Defence Minister Nirmala Sitharaman and Finance Minister Arun Jaitley will call on the King, sources said.
Mr Wangchuck arrived in New Delhi on Tuesday on a four-day visit to India. He is accompanied by his wife, Queen Gyaltsuen Jetsun Pema Wangchuck.'
The visit is in keeping with the long-standing tradition of regular high-level exchanges between the two countries. The Bhutan King's visit would provide an opportunity to both the sides for reviewing the entire gamut of bilateral cooperation.
Importantly, the golden jubilee of the establishment of diplomatic relations between the two countries will be celebrated next year.
In an appropriate response to King's visit and making a special gesture on her part, Ms Swaraj received the royal family at the airport.
"Special gesture for a valued friend. EAM @SushmaSwaraj receives Their Majesties, The King, The Queen and The Gyalsey (Prince) of Bhutan," External Affairs Ministry spokesperson Raveesh Kumar tweeted.
Notably, the Bhutanese King's visit comes weeks after the stand-off between India and China at Doklam plateau in Bhutan has cooled off.
The standoff that had triggered a big row between Indian side and Chinese Army in June over Chinese moves to build a road in an area claimed by Bhutan, ended in August, with both India and China deciding to "disengage" from the face-off point.
Mr Modi will host a dinner in honour of the royal family, a statement from the MEA said.