Paz, a senator from the Christian Democratic Party, won 54.6 per cent of the vote, ahead of Quiroga's 45.4 per cent, according to early results from Bolivia's electoral tribunal.
But Paz's party did not win a majority, forcing him to forge alliances to govern effectively.
The new president takes office on November 8.
The 58-year-old senator's win marks a historic shift for the South American country, governed almost continuously since 2006 by Bolivia's Movement to Socialism, or MAS, which once enjoyed overwhelming support from the country's Indigenous majority.
Paz's moderate platform - pledging to maintain social programs while promoting private sector-led growth - appeared to resonate with left-leaning voters disillusioned by the ruling MAS, founded by former President Evo Morales, but wary of Quiroga's proposed austerity measures.
Support for MAS cratered in the August first round amid a deepening economic crisis.
"This election marks a political turning point," said Glaeldys Gonzalez Calanche, analyst for the Southern Andes at International Crisis Group.
"Bolivia is heading in a new direction," she said.
Outside a polling station in La Paz, Lourdes Mendoza said she had grown weary of the MAS era.
"My children were born and raised with a single government," she said.
"I hope they can see other possibilities and alternatives."
Bolivia's fragile economy dominated the runoff campaign. Once plentiful natural gas exports have plummeted, inflation is at a 40-year high, and fuel is scarce.
Both candidates campaigned to roll back elements of the MAS era, state-led model, but differed over how drastically.
Paz favoured gradual reform, including tax incentives for small businesses and regional fiscal autonomy, while Quiroga proposed sweeping cuts and an IMF bailout.
"We're going for a new stage of Bolivian democracy in the 21st century," Paz told Reuters two days before the election at his family's ranch in the southern gas-producing region of Tarija.
"We're going to try to build an economy for the people," he said, one where "the state is no longer going to be the central axis".
Like his opponent, Paz has pledged to improve diplomatic ties with Western countries, including the United States, after years where Bolivia had aligned itself with Russia and China.
with AP
