27-year-old Modig, the current chair of the youth wing of Sweden's Christian Democrats, on Monday night left the migration agency in Havana where he was had been held since last week.
He has since received help from the Swedish embassy, according to foreign ministry spokesperson Anna Backlund.
"He can come home," she told AFP, while declining to say when Modig would be back in Sweden.
Modig was one of four people in the car that struck a tree on July 22nd in the southeast of Cuba, killing Paya, a winner of the Sakharov Prize for human rights, and another Cuban dissident, Harold Cepero Escalante.
Oswaldo Paya was one of Cuba's most prominent dissidents and reports have been circulating within the dissident community implicating that the Cuban authorities were in some way responsible for the accident.
Modig and Angel Carromero of Spain, who was driving the car, were slightly injured in the crash.
On Monday the pair told a press conference that the crash had indeed been an accident, denying reports to the contrary which included the claim that another car may have been involved.