Vakili Rad was released from a French jail two days after Iran released French academic Clotilde Reiss, who was arrested in the postelection crackdown and accused of spying. Twenty-four-year-old Reiss returned to Paris on May 16.
France has maintained that the two cases are unrelated. Vakili Rad's lawyer has also denied there was any trade.
Iran's semiofficial news agencies Fars and Mehr have posted pictures of Vakili Rad flashing the "Victory" sign upon his arrival in Tehran, where he was received with flowers from parliamentarian Kazem Jalili and government official Hassan Ghashgavi.
Vakili Rad, who spent 16 years in prison in France, was quoted by Fars as saying tearfully that he went through "hell" and happy he's now found "heaven."
Vakili Rad, a suspected Iranian agent, was convicted in 1994 for the 1991 assassination of Bakhtiar and an aide, Souroush Katibeh, and sentenced to life in prison with a chance of parole starting in June 2009.
Bakhtiar was Iran's prime minister shortly before the 1979 revolution. At the time of his death, Bakhtiar was living in a home outside Paris, where he was organizing opposition to the Islamic establishment under Ayatollah Ruhollah Khomeini.
Vakili Rad's lawyer has said he plans to work in a travel agency.
-- Golnaz Esfandiari