Foreign Minister Dipu Moni greeted the royal guests at the Hazrat Shahjalal International Airport at around 12.15pm.
According to the Ministry of Foreign Affairs, the minister will call on the king at Hotel Sonargaon later in the day.
The king and the queen are expected to call on the President and the Prime Minister on Feb 15 and 16, respectively.
The royal dignitaries will also visit places of historic importance.
This is second visit of the King Wangchuck to Bangladesh in less than two years. He first came as the guest of honour in Bangladesh’s 40th Independence Day celebrations in March 2011.
It is the first visit of Queen Gyaltsuen Jetsun Pema Wangchuck.
The King Jigme assumed the throne on Dec 9, 2006 at the age of 25 following abdication by His Majesty the Fourth Druk Gyalpo.
As the new king, he took upon himself the responsibility to establish democracy in Bhutan, the process of which was set in motion by the Fourth Druk Gyalpo.
The first parliamentary elections in Bhutan took place in 2008, and the Constitution of the Kingdom of Bhutan was adopted on July 18, 2008 in the first elected parliament.
The king was formally crowned on Nov 1, 2008, a year that marked 100 years of monarchy.
On May 20, 2011, King Wangchuck announced the royal engagement to the opening of the seventh session of the parliament.
The royal wedding took place on Oct 13, 2011.