Modi himself described the big victores as "very humbling and overwhelming".
Top leaders of the party, which captured power in UP with an unprecedented three-fourths majority, ascribed the win to the Modi government's "pro-poor policies" like Jan Dhan and demonetisation.
State BJP chief Keshav Prasad Maurya said the 'Modi wave' has catapulted the party to power in a big way.
Shah also asserted that the poll outcome will change the course of country's politics, marking the end of the politics of caste, nepotism and appeasement, and the beginning of the politics of performance.
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"Am overjoyed that BJP has received unprecedented support from all sections of society. Huge support from the youth is gladdening. Gratitude to the people of India for the continued faith, support and affection for the BJP. This is very humbling & overwhelming," he said in a series of tweets.
Addressing a packed press conference in the national capital, Shah said even opposition parties will admit that Modi has emerged as the country's "tallest leader since independence" after these victories.
Terming the poll verdict that marked the party's return to power after 15 years of political wilderness as historic, Finance Minister Arun Jaitley said it is an endorsement of the central government's policies and the poor have shifted their allegiance to the BJP.
"BJP's landslide victory in assembly elections has again established that people of India want development as pushed by Modi," he said.
Maurya said, "It is a Modi wave. The wave which started with 2014 Lok Sabha elections is continuing in 2017 and the momentum will go beyond the 2019 general elections."
Terming the massive win in Uttar Pradesh as the victory of
the policies of the Modi government and a thumbs up to its two-and-half year rule, Irani said in BJP merit wins over dynasty.
"This is the one political organisation which has made a humble citizen as the prime minister of the country," she said.
The Union Textile Minister also took a dig at Rahul and Priyanka, saying this is a failure of both the Congress leaders.
Attributing the victories to the Modi-led government's good governance and good delivery of promises, Union Law Minister Ravi Shankar Prasad said "The poor have given a decisive verdict that Modi is our leader and is working for our welfare."
Echoing similar sentiments, Union Minister Jitendra Singh said that the party won the elections due to the credibility of Prime Minister Narendra Modi that he enjoys across the country.
Meanwhile, Union minister Sanjiv Balyan denied that there was a division on the communal lines in the Uttar Pradesh.
"The election was fought on issues like law and order, development. The new generation understood the importance of bringing in the BJP," he said.
BJP MP from Gorakhpur Adityanath said that the SP-Congress alliance and the BSP have been rejected by the people in UP.
In a Twitter post, BJP President Amit Shah dedicated the victory to the party's "karyakartas who selflessly devoted themselves to expand our ideology and party base."
Union Ministers and BJP leaders also took to the microblogging site to post congratulatory messages and their assessment of the BJP's success in Uttar Pradesh and Uttarakhand and large gains in Manipur.
"BJP's electoral gain in Manipur is a reiteration of support by the people of the North East for PM @narendramodi ji's 'Act East' policy," Union Textiles Minister Smriti Irani tweeted.
Another leader Subramanian Swamy, a strong votary of the construction of a temple on the disputed site in Ayodhya, said he expects that the incoming Uttar Pradesh government will not oppose him on this front anymore.
Power Minister Piyush Goyal said the verdict was a "clear mandate" of Modi's "pro-Poor policies, good governance, deMonetisation and model of Development.
"Mandate is to serve the dalit, peedit, shoshit, vanchit, mahila & yuva who have reposed faith in our philosophy of Sabka Saath, Sabka Vikas," Goyal tweeted.