"I announce before you today, to ease the movement of the political process and the formation of the new government, the withdrawal of my candidacy in favour of brother Dr Haider al-Abadi," Maliki said in his Thursday address, adding that he had made the decision to preserve the country's unity.
The announcement came days after he refused to stand down and threatened to challenge the Iraqi president's decision to appoint Abadi as his successor.
"Maliki will withdraw the complaint against the president and will back the prime minister designate," Ali Mussawi, Maliki's spokesman, told AFP, referring to a lawsuit the outgoing prime minister had vowed to file.
Al Jazeera also reported that Maliki's move was influenced by the statement of Iraq's most senior Shiite religious leader, Ayatollah Ali al-Sistani.
Maliki had resisted months of pressure to step down. He had insisted on his right to form a new government based on the results of a parliamentary election in late April.