Yechury also exuded hopes that the "Kerala Model" will show the way to "prosperity, equality and united India".
"Salute to Kerala people. Defeated UDF and corruption. Rejected BJP's moves of communal and caste polarisation. LDF's success: United, strong and unitedly going straight to the People.
"Model Kerala. Shows the way for prosperity, equality and a united India," the Rajya Sabha member said on Twitter.
Hitting out at the NDA, the Left party also maintained the mandate it received means that people rebuffed "communal" politics of the BJP and its efforts to rally leaders of caste-based organisations.
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"The CPI(M) congratulates the people of Kerala for having voted the LDF to victory. The politburo conveys its warm greetings to all the workers and activists of the CPI(M) and LDF for this well-earned victory," it said.
Ruling Congress-led UDF in Kerala today suffered a setback in the civic elections, billed as the semifinal ahead of next year's Assembly polls, as CPI(M)-led LDF won a majority of local bodies, while BJP made inroads improving its tally.
BJP, which has so far failed to taste success in Assembly and Parliament elections in the state, won one municipality and 14 gram panchayats, but made significant inroads in several places especially Thiruvananthapuram, Ernakulam and Palakkad, posing stiff threat to both UDF and LDF.