Maliki's resignation comes after days of a tense political standoff in which Maliki's words and actions raised concern of a potential coup.
As recently as Wednesday evening, Maliki asserted it was his "ethical and patriotic duty" to remain in office until Abadi was confirmed by a federal court.
Maliki announced his resignation on Thursday evening.
"We commend Prime Minister Maliki for his decision to support Prime Minister-designate Haider al-Abadi in his efforts to form a new government in line with the Iraqi constitution."
It is unclear what prompted Maliki to concede, but there was mounting pressure from Iraqi politicians for him to step aside and allow Abadi to move forward with government formation.
Under Iraq's constitution, Abadi has 30 days from his nomination in which to form a unity government.
The White House said it is "encouraging" that Abadi's appointment has garnered support "from a wide range of leaders across the Iraqi political spectrum who have expressed their commitment to work with Dr. Abadi to form a broad, inclusive government with an agenda that can address the needs and legitimate aspirations of the Iraqi people."