Gandhi and Chidambaram were flying in a Falcon aircraft to Coimbatore in Tamil Nadu, sources at the Bengaluru International Airport said.
Gandhi is scheduled to address a public meeting at Erode later on Thursday evening.
An aircraft from the state-owned Hindustan Aeronautics Limited was sent to the airport for taking them to Coimbatore, they said.
Sonia Gandhi and Chidambaram later left in the aircraft sent by HAL, for Coimbatore, the sources said.