They said the selection of Sinha only shows that "government even today in all circumstances wants to use the CBI for its political benefits".
Kejriwal and Bhushan alleged that Sinha's moral integrity had been questioned and that he was reprimanded by the Patna High Court for favouring the then Chief Minister Lalu Prasad.
"The government wants to appoint a tainted person whom it can subsequently arm-twist for its own benefits," Kejriwal alleged.
Bhushan claimed the government "secretly" and "out of its own will" appointed the new CBI chief, whose "moral integrity had been questioned" earlier.
A controversy erupted over Sinha's appointment with BJP demanding that the Prime Minister keep it on hold, citing a recommendation by a Rajya Sabha panel on Lokpal that the selection be made by a collegium.
The government, however, said the selection of the 1974-batch IPS officer has been done in a "fair manner" following the "due process" and that the Prime Minister has got the authority to decide on one name, hours after BJP voiced its "strong disappointment" and "disapproval".