The incident took place at about noon on Friday at the Post Office on Main Street, Balerno, when a four-figure sum of euros and a three-figure sum of sterling were stolen.
The 26-year-old is expected to appear at Edinburgh Sheriff Court on Monday.
Police Scotland said they were still seeking two men in connection with the robbery.
They are urging anyone who has information which can help with their inquiries to get in touch.
Det Ch Insp Martin Maclean added: "In particular, we are eager to speak to members of the public who may have seen anyone acting suspiciously around Balerno before or after the robbery, in particular around a beige or golden Renault people carrier-style car.
"Also, anyone who may have seen two men acting suspiciously near to the Prison Officers' Club at Longstone roundabout, or on the nearby path to Stenhouse, shortly after the robbery."
In a separate development, police have charged a 34-year-old man in connection with an attempted armed robbery at a convenience store in the Restalrig area of Edinburgh on 13 February.
He is due to appear at Edinburgh Sheriff Court on Monday.
A 26-year-old man has been charged by police following an armed robbery in Edinburgh.