With 92 percent of the votes counted, Lugo, the left-wing opposition party candidate, had 41 percent of the vote to 31 percent for Blanca Ovelar, the governing Colorado Party candidate, The New York Times reported.
Ovelar conceded defeat at around 9 p.m., the newspaper said.
"Today we've written a new chapter in our nation's political history," said Lugo, 56, who will be the first Paraguayan president since 1946 from outside the Colorado Party.
Anticipating the outcome, Lugo supporters celebrated in downtown Asuncion, with fireworks and flag-waving, The Times said.
The race also featured a third candidate, retired army chief Lino Oviedo -- who recently had his prison sentence for allegedly attempting a military coup overturned.
Long lines were reported at some voting locations. The election was being monitored by dozens of observers from the Organization of American States.
Paraguayan President Nicanor Duarte, who could not seek re-election after serving a five-year term, had accused Venezuela and Ecuador of interfering in the elections. Venezuelan President Hugo Chavez has denied any meddling, the BBC reported.