"Congratulate CM Nitish Kumarji and other leaders of Grand Alliance. Let us hope aspirations of the people of Bihar will be fulfilled," Chouhan tweeted.
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Meanwhile, Singh said Bihar has now stopped Prime Minister Narendra Modi's juggernaut.
He tweeted, "Congratulation to Nitishji, Laluji, Soniaji and Rahulji. Bihar had stopped the rath of Advaniji in 1991-92 and now Modi's. I congratulate the people of Bihar as well," he said.
RJD chief Lalu Prasad Yadav as Bihar Chief Minister had stopped BJP patriarch L K Advani's rath (chariot) yatra to Ayodhya from Somnath in Gujarat, at Samastipur in Bihar in October 1990, contending that it will flare up communal frenzy.
The JDU-RJD-Congress alliance is set for massive victory in the 243-seat Bihar Assembly polls, trouncing the BJP-led grouping.