Vajpayee had resigned just 13 days after being in power due to lack of numbers.
This will be the fourth stint for Yeddyurappa as the chief minister -- the last one was after the May 2018 assembly polls.
Yeddyurappa claimed Kumaraswamy would fail to save the coalition government.
Yeddyurappa expressed confidence that there is a strong wave in favour of his party.
In a low key homecoming, former Karnataka Chief Minister B S Yeddyurappa on Thursday formally rejoined the Bharatiya Janata Party on Thursday, more than a year after he deserted the party and floated his own outfit.
Bookanakere Siddalingappa Yeddyurappa has navigated the choppy waters of politics with the consummate ease of a seasoned oarsman, defying tidal waves of adversity
He said a volcano is waiting to erupt in Cong-JD(S) alliance.
This has been the CM's shortest stint in power -- three days.
In BS Yeddyurappa's constituency, Shikaripura, many question BJP's 'sidelining' of its chief ministerial candidate.
"A new era of development will start from now onwards," said BJP's Karnataka president B S Yeddyurappa soon after the H D Kumaraswamy-led coalition government lost the confidence vote.
Yeddyurappa lacks the Karnataka BJP's unqualified support and Shah knows that.
In the tape, released hours ahead of the crucial floor test, the current CM is allegedly heard speaking to Congress MLA from Hirekerur B C Patil over phone.
In a letter to NDA Chairman and BJP veteran leader L K Advani, with whom he shares an uneasy relationship, Yeddyurappa requested him to involve Karnataka Janatha Party in all the deliberations of NDA by inviting it to all the meetings.
The BJP is has set its sight on regaining power by winning 150 out of 224 assembly seats.
BJP's chief ministerial candidate said that winning each assembly constituency was important for the party.
Opening a new chapter in Karnataka politics, former Chief Minister B S Yeddyurappa On Sunday formally launched Karnataka Janata Party and took over as its president at a massive rally in north Karnataka.
Yeddyurappa has 15 days to prove his majority in the assembly.
Former Karnataka Chief Minister B S Yeddyurappa on Friday came down heavily on the Bharatiya Janata Party leadership while lavishing praise on the Congress.
Chief Minister Siddaramaiah asked Modi to "walk the talk", posing four questions, including appointing an "untainted person" as Bharatiya Janata Party's chief ministerial candidate in the state whereas Yeddyurappa tweeted with a tagline #Date2Answer asking, "Why did you quash all the powers of Lokayukta and make it a toothless body?"
The Special Lokayukta court in Bengaluru summoned former Chief Minister B S Yeddyurappa even as it rejected a B report and ordered a further probe against V Somanna, the former CM's closest aide.
'Justice is done, I stand vindicated...' Yeddyurappa tweeted.
The Bharatiya Janata Party on Monday tried to put a brave front about the political muscle-flexing by former Karnataka Chief Minister B S Yeddyurappa, who is trying to appoint his preferred candidate as his successor. The party leadership believes Yeddyurappa's clout has dipped after he was forced to resign on Sunday.
Under attack from the Congress and the Janatha Dal Secular, while also battling threats of being ousted, Karnataka Chief Minister B S Yeddyurappa on Monday said his government enjoyed majority. He said there was no need for 'Operation Lotus' under which opposition members of the legislative assembly were lured to the Bharatiya Janata Party.
The party is hopeful that the return of the former Karnataka chief minister will boost its performance in the 2014 Lok Sabha elections.
Yeddyurappa, 74, an influential Lingayat leader, had led the saffron party to its maiden victory in the southern state in 2008, but was forced to resign following charges of corruption against him.
Karnataka Chief Minister B S Yeddyurappa said on Wednesday that any expansion of his ministry "was not on the cards for now" in the wake of speculation that he was trying to reinduct Shobha Karandlaje who was dropped from the Cabinet last year apparently to quell dissidence by the Reddy brothers.
The Bharatiya Janata Party has suspended B Y Raghavendra, son of B S Yeddyurappa from the party.
"I seek support of all legislators and I ask them to vote for me by exercising their conscience just as Indira Gandhi did in a Presidential election," he said.
Hitting out at the Bharatiya Janata Party leadership for the "ill-treatment" meted out to him, former Chief Minister B S Yeddyurappa on Friday charged party President Nitin Gadkari with failing to keep his promises.
Karnataka Chief Minister B S Yeddyurappa on Monday said problems arising out of dissident activities that recently gripped his government are over and the focus now is on relief works in flood-hit areas.
Serving anxious moments to the Bharatiya Janata Party government in Karnataka, party MLA Basavaraj Patil Attur, a known loyalist of former chief minister B S Yeddyurappa announced that he would resign his assembly membership on Friday.
Facing fresh trouble after the Supreme Court ordered a Central Bureau of Investigation probe into his alleged role in illegal mining, former Karnataka Chief Minister B S Yeddyurappa on Saturday held consultations with his loyalists on his political future.
The ruling Bharatiya Janatha Party in Karnataka finds itself in doldrums following the launch of a new political outfit by former chief minister B S Yeddyurappa last Sunday. Like always it is going to be a major caste factor that will come into play in the changed political scenario in Karnataka.
Many well wishers of Yeddyurappa are still hopeful that he will go back to the BJP fold, says Vicky Nanjappa
The special Central Bureau of Investigation court has rejected the anticipatory bail plea filed by former Karnataka Karnataka chief minister B S Yeddyurappa. Yeddyurappa, who is being probed by the CBI for his alleged role in illegal mining, had sought anticipatory bail apprehending arrest.
Angry BJP workers flung chairs and other furniture and raised slogans against party president Amit Shah and even tried to stop the cars of Vijayendra and other leaders as they were leaving.
In a renewed bid to get the party to reinstate him as chief minister, Bharatiya Janata Party Karnataka strongman B S Yeddyurappa today convened a meeting of his loyalists, including BJP legislators and members of Parliament, here to remind the central leadership of its promise to give him justice.
The Central Bureau of Investigation is conducting raids at the Bengaluru residence of former Karnataka Chief Minister BS Yeddyurappa as part of its ongoing probe into alleged illegal mining. Searches area also on at the residences of his two sons and son-in-law.
In a renewed bid to get the party to reinstate him, former Chief Minister of Karnataka B S Yeddyurappa has decided to move his members of Legislative Assembly to a resort on Monday.