Santos won the first round of the presidential poll on May 30 with 47 per cent of the vote against 22 per cent for Mockus, who runs for the Green Party.
Colombians associate Santos with several successful operations during his time as defence minister.
In March 2008, the military attacked the Revolutionary Armed Forces of Colombia (Farc) in Ecuador and killed Raul Reyes, the group's number two.
Operation Jaque in July the same year rescued 15 high-profile hostages, including French Ingrid Betancourt.
Uribe has used billions of dollars of aid from the US in a battle against Farc, and has managed to push them away from the main cities.
But the rebels have said they will keep up their fight against the government no matter who wins.
"People can vote for whom the want," Commander Duber of Farc told Al Jazeera on the eve of the election.
"But we will continue fighting. The ideology of the Farc is to win or die, that¹s what Che Guevara said."
"If there are conditions for peace talks then we could sit down and talk. But it¹s difficult. Santos has killed lots of innocent people while trying to kill us."
Whoever wins the presidential runoff will have to tackle the region's highest unemployment rate, a stubborn fiscal deficit and tensions with neighbouring Venezuela, where a trade dispute is weighing on Colombia's economic recovery.
Mockus has made a series of comments that led voters to question his ability to manage the military and Colombia's foreign relations.
At one point he suggested disbanding the military and then backtracked.
He also suggested he would have no choice but to extradite Uribe if an Ecuadorean court convicted him of wrongdoing in a 2008 cross-border raid. But in reality, presidents can deny extradition requests.
The mathematician and philosopher has also alienated voters by promising a tax