They head the Janata Dal (Secular)-Bharatiya Janata Party coalition government, which toppled the Dharam Singh-led Congress-JD(S) coalition government on January 28.
Kumaraswamy, son of former prime minister Deve Gowda, has gone against his father's wishes by joining forces with the BJP.
The coalition has entered into a power-sharing agreement, whereby Yediyurappa will take over as chief minister in 20 months.
Complete coverage: Karnataka - A coalition's fall
Picture: Karnataka Photo News