Poppy Scotland tins were reported stolen with the first alleged incident in Portobello on 1 November and a further two a week later.
Two other reported incidents took place in Musselburgh on 5 and 6 November.
The men, aged 27 and 35, are due to appear at Edinburgh Sheriff Court at a later date.
Two men have been charged in connection with the alleged theft of charity collection boxes from separate locations in the east of Scotland.