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Mr Siddaramaiah and DK Shivakumar attended the legislature party meeting where the formal election took place. They have also met Governor Thaawarchand Gehlot and staked claim to form government. The oath ceremony will take place at 12.30 PM on May 20.
Sources said there is a rough understanding of a 50:50 power sharing, under which Mr Shivakumar can succeed Mr Siddaramaiah in the top post halfway through the term.
But sources said this will hinge on the Congress's performance in the state in next year's general election. Karnataka has 28 parliamentary seats, making it one of the battleground states.
Both the leaders are expected to be in Delhi today to discuss names for the cabinet with the national leadership.
The five-day impasse over the top post was resolved after intervention by Congress's former president Sonia Gandhi, and DK Shivakumar was persuaded to accept the post of Mr Siddaramaiah's deputy. In addition, he would also have the control of the party and get his pick of six ministries.
Mr Shivakumar, who was refusing to budge from his demand for the top post, had ultimately agreed to "sacrifice for the party". In an interview to NDTV, he said, "We left it to the high command, they decide. It is the party's interest over personal interest. I have to accept the high command's decision".
Asked whether it was Sonia Gandhi's intervention that made him change his mind, Mr Shivakumar said, "I don't want to bring Mrs Gandhi or the Gandhi family into this. I just met Rahul (Gandhi) ji. I met Mallikarjun Kharge. I met AICC (All India Congress Committee) office bearers, that's it."
DK Suresh, Congress MP and Mr Shivakumar's brother, however, told NDTV that they were "not happy". "My brother wanted to be Chief Minister. We are not happy with this decision," he said.
The Congress has slammed BJP allegations of chaos in the party, saying they believe in "consensus, not dictatorship". The BJP's Basavaraj Bommai had alleged that the five-day public deadlock over the top post showed a "lack of unity" in the Congress.
The question of Chief Ministership and cohesion in the party is crucial for the Congress in the run-up to the general elections next year. While Mr Shivakumar has a following among the politically crucial Vokkaliga community, Siddaramaiah has the support of the AHINDA platform -- an old social combination of minorities, Other Backward Classes, and Dalits, which had overwhelmingly supported the Congress.
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