The Uruguay midfielder is on his way to London to complete his medical with the Gunners after his nation's World Cup exit.
Torreira spoke to Uruguayan media at the airport ahead of his flight to London.
He told Telenoche: "I would have been very happy to be able to return to Uruguay with my teammates, but this is a fantastic opportunity [to join Arsenal] and I do not want to waste it."
His Arsenal medical is due to take place on Monday.
Torreira will then return to Uruguay after the medical in order to celebrate a World Cup campaign in which his nation reached the quarter-finals for only the second time since 1970.