The release of this cash may bring to an end the 16-year case on the funds.
Gen. Abacha died in office in 1998 after a five-year iron-fist rule. He was seen as extremely corrupt and faced criticism over his human rights abuses.
The decision to return the funds followed a July 2014 deal between Nigeria and the Abacha family.
Under the agreement, the funds would be confiscated and returned to Nigeria, while 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 organisation, 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 organisation.
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 cash issue 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 Gen. Abacha while he was in power.