The former president of the Venezuelan Football Federation, who was also an executive committee member of South American organising body CONMEBOL, was among those arrested in Zurich in May.
Esquivel, who is accused of receiving millions of dollars worth of bribes in relation to the sale of broadcast rights for the Copa America finals in 2007, 2015, 2016, 2019 and 2023, will now be extradited after the Swiss Federal Office of Justice (FOJ) gave its approval.
"The Venezuelan citizen has 30 days in which to appeal to the Swiss Federal Criminal Court against the FOJ's ruling," an FOJ statement released on Wednesday confirmed.
Last week, the extradition of former CONMEBOL vice-president Eugenio Figueredo was approved, pending any appeal from the 83-year-old.
Ex-FIFA vice-president Jeffrey Webb has already agreed to face corruption charges in the US and is under house arrest while on bail, having pleaded not guilty.
