The airport was originally named called Gauchaur Airport, after the area of Kathmandu where it was situated. In Nepali, "Gauchaur" refers to a place where cows graze. The formal beginning of aviation in Nepal is generally placed at Gauchaur in 1949 with the landing of a Beechcraft Bonanza carrying the Indian ambassador, although there are disputed claims that Simara Airport existed in some form as early as 1946.

The first flight into Gauchaur occurred on 23 April 1949.

The first charter flight took place between Gauchaur and Calcutta, in a Himalayan Aviation Dakota on 20 February 1950.

On 20 February 1950, an Indian registered Dakota DC-3 commenced the first ever scheduled service, linking Kathmandu to Patna, Kolkata and Delhi.

In 1950, King Tribhuvan took refuge at the Indian embassy in an attempt to overthrow the Rana dynasty. Gyanendra Bir Bikram Shah, the four-year-old grandson of Tribhuvan was crowned the new king. On 10 November 1950, two Indian planes landed at Gauchaur Airport and carried the young king along with his grandfather to Delhi. After the Delhi Accord, the Rana regime ended and King Tribhuvan landed at Gauchaur Airport as the monarch on 18 February 1951, bringing a return of democracy in Nepal.

In 1952, the first scheduled domestic flights commenced to Bhairahawa, Biratnagar, Pokhara and Simara.

On 15 June 1955, the airport was inaugurated by King Mahendra and renamed Tribhuvan Airport in memory of the king's father. The airport was again renamed to Tribhuvan International Airport in 1964.

In 1957, the original 3,700 feet (1,100 m) grass runway 16/34 was re-laid in concrete. In 1964, the former runway 16/34 was abandoned for a newer 6,600 feet (2,000 m) runway 02/20. The new runway was extended from 6,600 to 10,000 feet (2,012 to 3,048 m) with the joint effort of the Asian Development Bank (ADB) and the OPEC in 1975. The runway was re-strengthened in 1981.

In 1961, Queen Elizabeth II landed in a Dakota plane for her first visit to Nepal, one of the most high-profile arrivals at the airport.

In 1967, Tribhuvan International Airport received its first jet aircraft, a Lufthansa Boeing 707 and 1972, the Nepali flag carrier, Royal Nepal Airlines commenced jet operations from the airport with a Boeing 727. The same year, Nepali personnel took over air traffic services from the Indian personnel.

In 1985, the extension apron of runway 02/20 was overlaid. The development of the terminal building was commenced in the same year. In 1987, the construction of the Airlines Operation and Control Tower building was completed and the taxiway was overlaid. In the same year, on 11 October, Nepal witnessed the first ever landing of the Concorde. In 1989, the construction of the terminal building was completed and on 18 February 1990, the newly built TIA complex was officially inaugurated by King Birendra Bir Bikram Shah.

In 1992, Necon Air, Nepal's first private airline commenced domestic operations from TIA with a Hawker Siddeley HS 748.

In 1997, airport surveillance radar (ASR) and secondary surveillance radar (SSR) came into the operation. The installation of radar surveillance was proposed by Japan in 1994, following the crash of Thai Airways Flight 311 and Pakistan International Airlines Flight 268 in 1992, which together claimed the lives of 280 people, including 17 high-level Japanese diplomats. On 9 September 1998, Prime Minister Girija Prasad Koirala officially inaugurated the radars.

In May 2007, Austrian Airlines discontinued its flight to Vienna, Nepal's last direct air link to Europe. In September 2013, Turkish Airlines launched direct flights from Istanbul to Kathmandu, re-establishing Nepal's connection with continental Europe.

In August 2013, the airport's only runway had to be closed for wide-body aircraft because the runway, which was in disrepair, could no longer withstand their weight.

In 2016, a new domestic terminal of 6300 m2 (67,813 sq. ft.) was opened, replacing the old terminal building of 2200 m2 (23,681 sq. ft.). The new facility is a temporary structure, and it cost Rs. 119.8 million to house passengers and office space for 15 local airlines.

In 2020, the runway was extended to 3,350 metres (10,990 ft 10 in), the departure hall was expanded to accommodate 1500 more passengers, the arrival area was extended to a lower level and the immigration hall was facelifted.

In 2022, the airport extended its domestic terminal, with the new section of the building being exclusively used by Buddha Air.

In September 2025, the airport was briefly shut down amidst anti-government protests.