The New York-based bank said Pandit would take over as CEO effective immediately.
"The combination of his deep executive experience and long history as a strategic thinker makes him the outstanding choice to be Citi's CEO," Robert Rubin, Citigroup's acting chairman since last month, said in a prepared statement.
Tuesday's announcement comes after much speculation that Pandit would assume the throne at Citigroup - one of the companies on Wall Street hardest hit by the ongoing credit crisis.
Since the summer, Citigroup has suffered billions of dollars of writedowns due to bad mortgage bets and witnessed the departure of former CEO Charles Prince.
In addition to announcing the appointments of Pandit and Bischoff, the company also said that Rubin, who served as Treasury secretary during the Clinton administration, will return to his previous role as a director.
To succeed him in the chairman's post, Citigroup picked the 66-year-old Bischoff, formerly head of Citi's European unit. He was named interim CEO on Nov. 4 following the departure of Prince.