Pawan Kuamr Bansal and Ashwani Kumar had resigned from the respective posts Friday night. President Pranab Mukherjee has accepted the resignations, the communique added.
Joshi is presently the surface transport minister and had earlier held the additional charge of railway ministry when Mukul Roy quit after Trinamool Congress left the UPA- II government.
Sibal is presently the communications and information technology minister.
While Bansal's nephew was arrested by the Central Bureau of Investigation (CBI) for allegedly taking a bribe for the appointment of a member of the Railway Board, Ashwani Kumar has come under attack in the Supreme Court for vetting the CBI report on the allocation of coal blocks.