The Congress, which in alliance with the JD(S) had made a bid to form the government in the state, referred to a 2011 tweet of Prime Minister Narendra Modi seeking the recall of the then Karnataka governor and said, "We agree".
Modi and his BJP had sought the recall of the then governor, H R Bhardwaj, alleging that he was "harassing" the BJP-led state government and "acting in a partisan manner".
Yeddyurappa was administered the oath alone, hours after the Supreme Court refused to stay his swearing-in.
In a rare post-midnight courtroom battle, the Congress-JD(S) combine made a desperate legal push to stall the government formation.
Yeddyurappa has 15 days to prove his majority in the Assembly.
The BJP has 104 MLAs in the House, eight short of the magic figure of 112.
The Congress today termed Yeddyurappa's oath as chief minister of Karnataka "farcical" and said the party's "irrational insistence" on forming government in the southern state when it did not have the numbers made a mockery of the Constitution.
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