Abacha ruled oil-rich Nigeria with an iron fist from 1993 until he died in 1998.
The economy grew under his rule, though he was seen as extremely corrupt and faced criticism over his human rights abuses in the oil-rich nation.
The decision to return the funds follows a July 2014 deal between Nigeria and the Abacha family.
Under the agreement, the funds would be confiscated and returned to Nigeria, while the Nigerian government in Abuja would drop its case against the deceased dictator's son Abba Abacha.
The $380 million had been placed in several accounts abroad that were controlled by the Abacha family, which is considered a criminal organization, the Geneva prosecutors' office said in a statement.
The money was seized in 2006 in Luxembourg, under orders from the Swiss authorities.
The Abacha family had also placed some $500 million (530 million euros) in Swiss banks, though those funds have already been returned to Nigeria.
The $380 million will be returned under the World Bank's supervision, said the prosecutor's office.
The authorities have also decided to drop their case against Abba Abacha, which began in 1999.
In 2012, the dictator's son was handed a one-year suspended prison sentence for participating in a criminal organization.
Switzerland's top court cancelled the sentence in May 2014, citing procedural reasons.
The Geneva prosecutor's office on Tuesday said Abba Abacha has already been detained for 561 days from 2004 to 2006, without receiving compensation.
The Abacha affair began in 1999, when Nigeria asked the Swiss judicial authorities to help it recover $2.2 billion ($2 billion euros) embezzled and siphoned off by Sani Abacha while he was in power.