The run-off will take place between former foreign minister Abdullah Abdullah and ex-World Bank official Ashraf Ghani.
None of the candidates polled more than 50 per cent of votes during the first round in April. Abdullah got 45 per cent of the votes while Ghani received 31.6 per cent, as per the final results, which came amid fraud allegations.
On the eve of elections, tight security arrangements was seen across the capital city with heavily armed security personnel checking all vehicles.
"We hope our security measures will be even better than the last election", the Afghan army's chief of staff General Sher Mohammad Karimi said.
Also Read
Authorities said nearly 400,000 soldiers and policemen have been deployed for election security.
In a statement, Taliban warned people to "remain far away from the polling stations... Lest you should be hurt or killed."
Interestingly, Taliban insurgents failed to launch a single high-profile attack during the first-round in April when people turned up in large numbers to cast their vote.
It is the first time that Afghanistan will witness the second round of presidential elections.
It comes as the US-led NATO troops withdraw after more than a decade of fighting the Taliban, who were thrown out from power in 2001 for sheltering Al-Qaeda masterminds behind the 9/11 terror attacks.