The man, who is of Bulgarian origin but resides in England, faces charges of defacing cultural heritage that carry a possible sentence of two to five years in prison.
He was identified after the Colosseum Park Authority was alerted to the incident by a video allegedly filmed by the pair and posted on social media.
There have since been two further acts of vandalism against the 2000-year-old monument.
Rome Carabinieri police on Saturday cited a 17-year-old German student caught carving something into a wall on the ground floor of the Flavian amphitheatre.
Previously a 17-year-old Swiss girl was caught after being filmed scratching her initials into a stone at the ancient arena.
ANSA
