Lasso, with some 52.5 percent of the votes, had a 5.5 percent lead over Arauz in the second round of voting held on Sunday.
The Socialist candidate conceded defeat after more than 96 percent of the votes had been counted showing he had gained 47.4 percent of the votes.
Arauz, who topped the first round of the voting, said he had expected to win the presidency.
His mentor is former leftist president Rafael Correa.
Correa is living in Belgium after receiving an eight-year prison sentence on corruption charges in his home country.
Lasso, a former banker, is a proponent of tax cuts and austerity measures.
He believes new tax cuts will boost the economy and backs measures to reduce public debt. He has formerly run for the presidency twice.
Lasso will succeed current President Lenin Moreno, who congratulated the president-elect in a tweet and wished him success. The outgoing president is deeply unpopular.
Moreno's decisions to implement austerity measures and cut oil subsidies led to mass protests in 2019.
Lasso's rise to power comes as the Latin American country grapples with the health and economic consequences of the coronavirus pandemic, which has killed more than 17,000 people in Ecuador and strained the country's healthcare system.