An emotional Yeddyurappa resigned as Chief Minister of the southern state without facing a trust vote, ordered by the Supreme Court.
"Today, the people's mandate has prevailed over money power," Mr Yadav wrote on Twitter.
"Those who thought they could buy everyone have learnt the lesson that there are still people left who don't consider politics a business," he tweeted.
"The central government should also resign on moral grounds," he added.
Jubilant scenes were witnessed at the Congress office after Mr Yeddyurappa resigned as Karnataka Chief Minister.
Senior Congress leader Pramod Tewari and his daugher Aradhana Misra, who is an MLA, distributed sweets among party workers.
"It's a victory of democracy," Mr Tewari said.
Mr Yeddyurappa's resignation will pave the way for the formation of a government led by JDS state chief HD Kumaraswamy, who has the backing of the Congress. The newly formed alliance has claimed support of 117 MLAs in the 224-member assembly with an effective strength of 221.
Polling for two seats was not held due to various reasons, while Mr Kumaraswamy won from two places.