Wilfried Martens, a former prime minister, was asked to help finding a solution to Belgium's political crisis and had accepted the task, the statement from the palace said.
After Leterme handed in his resignation, the king conducted a series of meetings with Belgian politicians.
It is likely that the leading political parties will now seek to broker a coalition without immediately calling for elections, as the need for government action to counter the financial crisis is urgent.
After his resignation was accepted, Leterme, a Christian Democrat, said in a statement that he had spared no effort in trying to overcome Belgium's power-sharing crisis since he won the elections in June 2007.
He also said he hoped to be able to prove his innocence over the scandal the Belgian media has called "Fortisgate."
"I hope with all my heart to have, over the weeks to come, an honest and calm opportunity to refute in a transparent way all the accusations levelled against me and my collaborators," he said.
A senior Belgian judge has said that, after a preliminary inquiry, he had "strong indications" but no legal proof that Leterme's office had tried to influence an appeals court.
Fortis, one of Belgium's biggest banks, was carved up by the Dutch, Belgian and Luxembourg governments with France's BNP Paribas buying the Belgian operations after a $16.1bn cash injection failed to calm investors' concerns over its health.
Minority shareholders launched a legal action against Belgium's government over the sale.
Leterme's office stands accused of trying unsuccessfully to persuade the appeals court not to grant a legal appeal by the shareholders against the break-up.