Santos, 58, told cheering crowds in a Bogota hall decked with the white banners of his U party that "Colombia expects so much from us and we are not going to let them down".
He added: "This is your victory too, President [Alvaro] Uribe."
Santos has promised to continue the security and pro-business policies of Alvaro Uribe, the outgoing president who was unable to run for re-election after a constitutional court barred him from seeking a third term.
Uribe's second four-year term was marred by scandals over corruption and human rights abuses, including arrests of legislators for colluding with death squads and a probe into state spies illegally wiretapping journalists and judges.
But he remains popular for battling the left-wing Revolutionary Armed Forces of Colombia (Farc) fighters, using billions of dollars in US aid to push them away from Colombia's main cities.
The fighers have said, however, that they will keep up their fight against the government.
"People can vote for whom the want, but we will continue fighting," Commander Duber of Farc told Al Jazeera on the eve of the election.
"The ideology of the Farc is to win or die, that's what Che Guevara said.
"If there are conditions for peace talks then we could sit down and talk. But it's difficult. Santos has killed lots of innocent people while trying to kill us," he said.
Santos, however, gave no indication he would pursue peace talks, saying in his victory speech that "the time is up for the Farc".
"We will keep fighting against the enemies of the state," Santos said.
As defence minister, Santos oversaw several successful operations against Farc, including the March 2008 attack on the fighters in Ecuador which killed Raul Reyes, the group's deputy leader.
In July the same year the military successfully rescued 15 high-profile hostages held by Farc, including Ingrid Betancourt, a former presidential candidate.
But in a sharp reminder of the lingering conflict, seven police officers died in a landmine blast near the Venezuelan frontier on election day, and troops killed six guerrillas in clashes in a central area.
The next president's tenure as defence minister was also tainted by charges that troops killed civilians to artificially lift combat tolls.
Those allegations cost the army chief and 27 officers their posts, but Santos survived and said he had moved to halt the so-called "false positive" killings.
Santos, who has also served as finance minister and helped Colombia over a 1990s fiscal crisis, must also tackle double digit unemployment, a stubborn deficit and a costly public health system as the economy tries to recover from the global crisis.
|Deadly violence on election day was a sharp reminder of the conflict with Farc [AFP]
He must also tackle tense relations with Hugo Chavez, the Venezuelan president, with battered trade ties already weighing on Colombia's economy.
The two men, who Santos says are like "oil and water", have already clashed repeatedly.
Jorge Restrepo, a political analyst, told Al Jazeera that "Santos is seen as someone who can be trusted with the economy".
"He was viewed as a safe pair of hands in the previous economic crisis and will be expected to push through reforms that will assist in pushing down the unemployment rate in this country," he said.
Santos, a US and British-educated economist, fell just shy of the simple majority needed to avoid a run-off in the first round of voting last month, taking 47 per cent.
Mockus, the Green party candidate, ran an anti-corruption campaign that many Colombians considered well-intentioned but naive.
He congratulated Santos and conceded defeat at his campaign headquarters on Sunday.
But he vowed that "the Green Party will be an independent force".
"There are millions of us who have found a new way to do politics," he said.