Colombia's outgoing conservative President Ivan Duque on Monday promised a "transparent and efficient" transition to the new administration led by Gustavo Petro.

Ex-guerrilla Petro, 62, made history on Sunday when he was elected as the first left-wing president in the crisis-torn South American country's history.

But with Duque and Petro occupying polar opposites on the political spectrum, there are fears the transition could be tense.

"Yesterday, we Colombians went to the polls, we expressed our points of view and the first thing one must recognize to defend democracy is the popular will," said Duque on Twitter.

"To the new president @petrogustavo, I expressed my support for a transparent and efficient transition."

Petro garnered 50.4 percent of the vote in Sunday's runoff, with millionnaire businessman Rodolfo Hernandez on 47.3 percent, missing out by 700,000 votes.

Hernandez immediately recognized his defeat as Petro ended 200 years of conservative and liberal political dominance.

In his victory speech, Petro promised "real change" for his country, based on "peace, social justice and environmental justice."

He vowed to "leave hatred behind, leave sectarianism behind."

Gustavo Petro has been elected as the first left wing president in Colombia's history
Gustavo Petro has been elected as the first left wing president in Colombia's history AFP / Juan BARRETO

Petro celebrated his victory in a huge theater in Bogota while thousands of his supporters descended on a rainy historic square in the center of the capital to rejoice.

The announcement of environmental activist and feminist Francia Marquez as the new vice-president was met with joy in her home town of Suarez in the southwestern department of Cauca.

As the first black woman to be elected to that post, her success was celebrated throughout communities with significant populations of Afro-descent, who make up around 10 percent of the country's 50 million people.

On Monday morning, El Espectador ran a headline lauding the "historic change," while also pointing to the many challenges facing Petro.

Former president Alvaro Uribe (2001-10), speaking on behalf of the traditional right-wing, which suffered a humbling first round defeat last month, said Petro would face determined opposition.

"To defend democracy, you have to respect it. Gustavo Petro is the president. One feeling must guide us: Colombia first," said Uribe on Twitter.

"A difficult stage in the national life is about to begin and we must prepare to face it with the necessary tenacity to defend our principles and values," added senator Maria Fernanda Cabal.

"It is not the time to conform, it is time to fight for our freedom."

Petro will assume office on August 7.