The BJP and IPFT together bagged 43 seats.
The elections in 59 seats in the 60-member Assembly were held on February 18. Polling was countermanded in one seat due to the death of a CPI(M) candidate.
The BJP with a tally of 35 seats secured majority on its own while its alliance partner, the Indigenous People's Front of Tripura (IPFT) captured eight seats, according to Election Commission (EC) sources.
The saffron party inflicted a humiliating defeat on the Left Front, which had never faced such a situation, even when it had lost power in 1988 to the Congress-Tripura Upajati Juba Samity combine.
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The BJP's spectacular performance came as a surprise for many as the party did not even have a councillor in Tripura.
It had secured less than two per cent votes in the 2013 Assembly polls in the state.
According to an EC source, the BJP, which contested in 51 seats in Tripura, has secured over 43 per cent of the votes.
Among the winning candidates in the BJP were Biplab Deb, its state unit president.
Its ally IPFT, which fielded candidates in nine seats, got nearly eight per cent votes.
The Left Front had lost in 1988 Assembly polls to the Congress-Tripura Upajati Juba Samity combine by just one seat.
The Congress had a disastrous performance in the state as it failed to win even a single seat.
Its vote share dipped to less than two per cent, the EC source said.
The Congress had won 10 seats in 2013 Assembly polls. Six of its MLAs had deserted the party in 2016 and switched over to the Trinamool Congress. They joined the BJP last year.
BJP leader Ram Madhav said that the people in the state have voted for a change.
"They have supported our slogan for change," he said, adding that the CPI(M) gave a "spirited fight".
BJP in-charge in Tripura and Assam minister Himanta Biswa Sarma said, "People were fed up with the Manik Sarkar government which has been ruling the state for more than two decades and wanted to get rid of the CPI(M) rule."
He also said the BJP's alliance with the tribal-dominated IPFT helped the saffron party.
Sarma also dismissed the suggestion that the minorities, particularly the Christians in the northeast, were against the BJP, saying the community "wholeheartedly" supported the party.
Sunil Deodhar, BJP's election in-charge in Tripura, said that the very first credit goes to Prime Minister Narendra Modi.
"Modiji has held four rallies in a small state like Tripura. The people of Tripura were starving for development," he said, adding they were waiting for a BJP government.
On the poll outcome, CPI(M) general secretary Sitaram Yechury said, "Tripura voters have given their mandate for a BJP-IPFT government in the state. We thank the people of Tripura for giving us the opportunity to serve them for the past 25 years."
He alleged that the BJP has used both "money and muscle power in Tripura".