The Society of Jesus chose Arturo Sosa Abascal, 67, of Venezuela in a ballot on Friday to replace Adolfo Nicolas of Spain, who is retiring.
It is the largest order of priests and brothers in the Catholic Church.
Argentine Jorge Mario Bergoglio became the first Jesuit and Latin American Pope in 2013, taking the name Francis.
The Catholic Church specialises in coming up with intricate ways of picking its leaders - and then giving those leaders memorable titles.
More than 200 Jesuit electors gathered here in Rome for four days of conversations known as "murmuratio" - or whispering.
These conversations ended in a vote - during which Arturo Sosa Abascal from Venezuela was picked as the new Superior General. The Jesuits' leader wears the simple black vestments of a regular priest. The clothes give the leader the unofficial title of the "Black Pope".
His election is a sign that the Catholic Church continues to look outside this continent for its leadership. His election will be welcomed by his fellow Latin American, Pope Francis, who spent many years himself as a Jesuit priest.
Father Sosa entered the Society of Jesus in 1966 and was ordained a priest in 1977, according to Catholic News Agency. It said he was appointed Superior of the Jesuits in Venezuela in 1996, guiding the nation through "the stormy waters" of Hugo Chavez's leadership.
The Jesuits were founded in 1540 by St Ignatius of Loyola.
The highly influential order now numbers about 17,000 and its members have strong roles in education and on human rights issues.
The Jesuits have elected a Latin American as their new leader, breaking a tradition of European heads dating back to their foundation in 1540.