In 1990, Tobgay received a bachelor of science in mechanical engineering from the University of Pittsburgh's Swanson School of Engineering after obtaining a scholarship from the United Nations. Tobgay also completed a master's degree in public administration from the John F. Kennedy School of Government at Harvard University in 2004.
Tobgay was a civil servant before he engaged in politics. He started his career in 1991 with the Technical and Vocational Education Section (TVES) of the Education Division in Bhutan. After his stint with the TVES from 1991 to 1999, Tobgay created and led the National Technical Training Authority (NTTA) from 1999 to 2003.
Tobgay also served from 2003 to 2007 in the Ministry of Labour and Human Resources as the Director of the Human Resources department. Tobgay resigned from the Ministry of Labour in February 2007 and entered politics to serve his duties for the reigning king, who established democracy in 2008.After the election in 2013, Tobgay became the Prime Minister of Bhutan through a secret ballot.
During Tobgay's campaign in the 2013 election, Tobgay focused on improving Bhutan with small promises. Instead of following in his predecessor's footsteps and promoting the Gross National Happiness, Tobgay pledged to give each village a power tiller, utility vehicles for each district and two national ambulance helicopters. Tobgay's election campaign focused on improving the economy which had then fallen to a record low of 2%. The campaign also promised strengthening rural economy, reforming education sector and empowering the local government.
On 17 December 2014, the King of Bhutan presented Tobgay with the Lungmar Scarf for his efforts put in for the wellbeing of nation being Prime Minister of Bhutan.
At a 2015 TED talk titled TEDxThimphu, Tobgay spoke about happiness and how Common the theme of happiness was talked about at other Ted Talks, including by Nancy Etcoff, and Silver Donald Cameron. In his speech, Tobgay emphasized that having a sense of purpose, identity, and security is important to become happy.
At a 2016 TED talk, Tobgay spoke about Bhutan's pledge to remain carbon neutral for all time. He shared his country's mission to put happiness before economic growth and set a world standard for environmental preservation. He spoke at the UN general assembly in 2017, resonating Bhutan's environmental achievements and the need of the world to unite to save the environment.
Tobgay was a co-founder member of the People’s Democratic Party and was responsible for establishing the Party as Bhutan’s first registered political party. At the 2008 election, the PDP only obtained two seats, with Tobgay winning one of the seats. In 2009, the PDP's leader Sangay Ngedup resigned from his position, and Tobgay took over as the party's leader. After the 2013 election, Tobgay was elected as Prime Minister of Bhutan by a secret ballot.
