Mr Shah assured the voters that the promises made in the party's election manifesto released on Sunday would be implemented.
"Seeing the atmosphere and campaigns after visiting various constituencies, I am rest assured that the BJP would form the next government in Tripura and it would be the 20th BJP-ruled state," Mr Shah told a news conference in Agartala.
"The party neither had MLAs in Manipur and Assam nor a strong organisational base, yet the huge popularity of Prime Minister Narendra Modi and the BJP's programme brought the party in power in those two north eastern states," he said.
Likewise, Tripura also would come to the BJP fold, he said.
The Left Front has been ruling the state for nearly 25 years continuously but Tripura lags behind in distribution of drinking water to households, healthcare services, power supply, infrastructure and attracting investments, he said.
The CPI(M)-led Left Front is in power in the north eastern state in a row since 1993. The Left was also in power between 1978 and 1988.
"Ten years and 25 years is quite a long time for developing the state. But Tripura remained backward. There are many BJP-ruled states which could make much more development in lesser time," he said.
Development would come only after the saffron party formed the next government, Mr Shah said.
CPI(M) cadres dictate terms to the police and government officials and law and order has collapsed, the senior BJP leader claimed.
But after seeing the rise of the BJP in the state, they were frustrated and resorted to violence against the BJP workers and leaders, he alleged.
"The BJP workers are ready to face the CPI(M) violence anywhere in the state," he said and appealed to police and government officials to work impartially.
Criticising opposition Congress, Mr Shah said the party was trying to divide the anti-Left votes in the state for favouring CPI-M, but that would not work.
He said Union Finance minister Arun Jaitely on Sunday published the manifesto of the party which promised that special economic zone (SEZ) would be set up in the state and smartphones would be given to the youth for free if the saffron party is elected to power.
Election to the 60-member Tripura Assembly would be held on February 18. The BJP is contesting in 51 seats, while its alliance partner Indigenous People's Front of Tripura (IPFT) has fielded candidates in nine seats.