Following the Libyan government's ultimatum, Salah Zahaf, Goeldi's lawyer, told the AFP news agency: "He will leave the embassy and turn himself in voluntarily," .
Zahaf said he expected Goeldi to be taken to Ain Zara prison near Tripoli.
He also said the defence plans to ask the court for an amnesty.
Relations between Libya and Switzerland have been strained since July 2008, when Hannibal - a son of Muammar Gaddafi, the Libyan leader - was arrested in the Swiss city of Geneva after two workers complained he had mistreated them.
The row escalated when Libya swiftly detained Hamdani and Goeldi and confiscated their passports.
It deteriorated further last year when a tentative political deal between Swiss and Libyan ministers fell through.