Shankar is a Karnataka Pragyavantara Janata Paksha (KPJP) MLA from Ranebennur Assembly segment in Haveri district, while Nagesh is an Independent MLA from Mulbagal segment in Kolar district.
Both the legislator took the oath in Kannada in the name of god.
State Chief Secretary T.M. Vijaya Bhakar conducted the proceedings of the brief oath-taking event in the 'Glass House' on the lawns of the Bhavan.
Shankar has become a minister for the second time after he was dropped in a minor cabinet reshuffle on December 22, 2018.
Incidentally, Shankar and Nagesh withdrew support to the coalition government on January 15 saying they were disappointed with its poor performance.
Contrary to expectations, a legislator from the Congress was not inducted into the 34-member ministry, which has one vacancy.
The two legislators were inducted from the 12-member quota of the JD-S, whose 10 MLAs are already in the ministry.
Of the 34-member ministry, the JD-S has filled 10 of the 12 cabinet posts and the Congress 21 of the 22 posts, as per the power-sharing agreement the post-poll allies have agreed to in proportionate to their strength in the Assembly.
As per the amended Constitution, a state government is entitled to have 34-member ministry, which is 15 per cent of the 225-member state legislative Assembly.
In the 225-member state assembly, including one nominated from the Anglo-Indian community, the BJP has 105, Congress 78, excluding speaker, JD-S 37 and one each from KPJP and Bahujan Samaj Party (BSP) and Independent.
In the May 19 two Assembly by-elections, the BJP wrested the Congress seat in Chincholi while the Congress retained the Kundgol Assembly segment in Hubli district.
"Instead of including our party's legislators, Kumaraswamy has decided to make Shankar and Nagesh ministers to prevent the opposition BJP from poaching them," a JD-S official told IANS.
A split verdict in the May 2018 Assembly elections resulted in a hung house, forcing the ruling parties to form a post-poll alliance to ostensibly keep the BJP out of power as it fell 9 short-off the halfway mark (113) for a simple majority.
As the ruling allies faced rout in the recent Lok Sabha elections, winning only one seat each against 25 of the 28 parliamentary seats by the BJP in the southern state, efforts have been on to ensure the fledgling coalition ministry survives and continues to complete its remaining 4-year term.