Abdullah has said he would not seek re-election after the anti-graft commission named him as a corruption suspect.
Abdullah, whose five-year term ends in May, and two of his colleagues are suspects in a case where a foundation linked to Bank Indonesia had illegally paid members of parliament.
He has denied any wrongdoing.
Indonesia's central bank has been the subject of various probes in the past decade, particularly over its controversial role in lending billions of dollars in emergency funds to banks during the height of the 1997-98 financial crisis.
Indonesia's parliament on Monday appointed Boediono, chief economics minister, as the next central bank governor.