The head-to-head election, scheduled for June 14, will choose a successor to President Hamid Karzai in Afghanistan's first democratic transfer of power.
Whoever wins will have to oversee the fight against a resilient Taliban insurgency as 51,000 US-led troops depart this year, as well as try to strengthen an economy reliant on declining aid money.
"After a thorough review, it is clear that no candidate has been able to win more than 50 percent and the election goes to a second round," said Ahmad Yusuf Nuristani, head of the Independent Election Commission (IEC).
Abdullah secured 45 percent of the vote on April 5, with his main rival Ghani on 31.6 percent, according to the final results, which came after weeks of deliberation over fraud allegations.
The 2009 election, when Karzai retained power, was marred by rigging in a chaotic process that shook confidence in the multinational effort to develop the country, and also marked a sharp decline in relations with the United States.
The run-off was originally scheduled for May 28, but ink and other material was damaged in an insurgent attack on the election authorities' warehouses.
"Some sensitive materials that were stocked at IEC headquarters for the second round were destroyed by the Taliban attack -- providing those materials again needs time," Nuristani said.
The UN mission in Afghanistan welcomed the results, but warned that the run-off would pose a test for candidates and election authorities.
"Candidates have a responsibility to call on their supporters to refrain from inflammatory rhetoric, intimidation, and threats," said UNAMA chief Jan Kubis.
"(They) must also instruct their supporters not to commit fraud on their behalf."
Both candidates were due to hold press conferences later today.
Abdullah this week received a major boost with the endorsement of third-placed Zalmai Rassoul, a close ally of Karzai, who has stayed publicly neutral in the election.