Family and colleagues said they felt great relief at the end of the crisis that added to tensions between Iran and the US.
Esfandiari was released on bail in August, picked up her passport and flew from Iran to Austria, where her sister lives, said her daughter, Haleh Bakhash.
"After a long and difficult ordeal, I am elated to be on my way back to my home and my family"
She was reunited with her husband and plans to spend about a week there before heading home to the US, Bakhash said.
Abdol Fattah Soltani, Esfandiari's lawyer, said she booked a flight immediately after getting her passport back on Sunday.
Esfandiari was prevented from leaving Iran since the authorities seized her passport in January and interrogated regularly. She was arrested and imprisoned in May until her 93-year-old mother posted bail using the deed to her Tehran apartment.
The Iranian intelligence ministry accused Esfandiari and the Wilson Centre of trying to set up networks of Iranians ultimately aimed at creating a "soft revolution'' in Iran, charges both her husband and the centre have denied.
Esfandiari is one of several Iranian-Americans who have been detained or are facing security-related charges in Iran.