Mirsad Bektasevic, a 28-year-old man of Bosnian descent from Kungälv, north of Gothenburg, was one of those arrested. The other was a 19-year-old of Yemeni origin, who was not immediately named.
The two were travelling by bus when they were seized on Thursday in the northern city of Alexandroupolis, near the Turkish border, according to police sources.
Inside their luggage were found two machetes, army uniforms and other "combat paraphernalia", the sources said.
Both men have been charged with carrying weapons and will go before a magistrate on Tuesday, police said.
Bektasevic was in 2005 convicted of conspiracy to commit a terrorist offence after security services raided his apartment and found large quantities of explosives, a suicide belt, and a video showing a man threatening terror attacks against the US Capitol and the White House.
He was sentenced to 14 years in prison but was released in 2011, after which he sought political asylum in Sweden.
The two men arrived in Greece by plane from Sweden "ten days ago", and travelled by bus to Thessaloniki and then to Alexandroupolis with tickets bound for Turkey, police said.