The 52 year-old was detained by Peruvian authorities at Lima airport on December 26.
Villeverde will, however, be unable to leave Peru until a ruling is made on his case, which could take up to a month.
In a written statement issued following his release, Villaverde said:
"I'm extremely grateful for all the support shown for me and my family. I am innocent and have already been cleared of these charges once."
Villverde is a city councilor in Sundsvall, northern Sweden, and was on his first trip to his homeland in 20 years to visit his mother who was reported to be in poor health.
In interviews, Villverde has described how he was labelled a terrorist after working with disadvantaged communities in Peru's mountain villages.
Villverde left Peru as a refugee in 1995, during a period of political violence prompted by the Sendero Luminoso Maoist guerillas.
Before leaving Sweden, he had received assurances from Peruvian lawyers that he could return to Sweden unhindered.