Janata Dal-Secular (JDS) leader HD Kumaraswamy and Congress state unit president G Parameshwara were sworn-in on May 23 as Chief Minister and Deputy Chief Minister.
The Congress high command will decide who among its legislators are to become ministers and which portfolio they will hold.
"Parameshwara is going to Delhi on Tuesday to finalise the 21 legislators of the Congress to be inducted into the ministry in consultation with party President Rahul Gandhi and state in-charge KC Venugopal," said Mr Radhakrishnan.
The party's high command will also recommend to the Chief Minister the portfolios to be given to the 22 Congress ministers, including the Deputy Chief Minister.
Similarly, Mr Kumaraswamy will decide names of the JDS legislators to be made ministers and the portfolios they will hold by Tuesday night in consultation with party supremo HD Deve Gowda and other senior leaders.
"Kumaraswamy will discuss the issue with all our legislators on Tuesday morning and short list the names of 11 MLAs to be made ministers and their portfolios. The list will be finalised in consultation with Gowda by Tuesday night," a JDS spokesman told IANS.
Besides Finance, the JDS will have Excise, Information, Intelligence, General Administration, Planning & Statistics, Public Works Department (PWD), Power, Cooperation, Tourism, General Education, Animal Husbandry & Fisheries, Horticulture & Sericulture, Small-Scale Industries, Transport and Minor Irrigation.
In the 225-member Assembly, including one nominated, the Congress has 78 MLAs, the JDS has 36 and the BJP 104, with three others.
Though the Congress retained Bengaluru's Raja Rajeshwari (RR) Nagar assembly segment in the election held later, it lost its legislator Siddu Nyamagouda in a road accident in Bagalkot district.
Election to one assembly segment (Jayanagar in Bengaluru south) is due on June 11 and vote count on June 13 after it was deferred owing to the death of BJP contestant BN Vijaya Kumar on May 4.
Mr Kumaraswamy had won the trust vote on May 25 by voice vote in the Assembly a week after the three-day BJP government fell when its Chief Minister BS Yeddyurappa resigned before the floor test as he fell seven votes short of the halfway mark.