The pair were arrested on December 11th, the day they arrived in Switzerland, after police were alerted about their behaviour.
A case was opened against the men, who were suspected of “the manufacture, concealment and transport of explosives or toxic gases” and of violating Swiss law prohibiting "groups like Al-Qaeda, Islamic State (Isis) and similar organizations".
They were kept in custody for 50 days and released at the end of January.
Quoting a September ruling from the Swiss prosecutor's office, news agency ATS said on Wednesday that the case against the men had been dropped and that they would receive damages of 11,000 francs ($11,100) and 12,500 francs ($12,600) respectively.
Their legal costs would also be paid by the Swiss government, said ATS.
Their arrests came during a time of heightened security in Geneva as the terror alert level was raised following the attacks in Paris in November.
At the time Geneva public prosecutor Oliver Jornot told the media that the men's vehicle "was at one point used to transport explosives" but that it did not necessarily mean it was the two suspects who did so.