Sorry, about a month ago I said this was not possible. I don't know what I was thinking. It is possible and correct.
Without a time period, this would not be correct. You could says: "The wars ended before I was born." Another correct one we have in the incubator: "The wars have ended."
Edit shown above.
The verb here is "end". "Stop" is not the same. It could mean "the wars stopped" but then they began again whereas "ended" means there are no others.
"The wars have finished." has been added as a translation.
Would a direct translation be "Οι πόλεμοι έχουν τελειώσει". The wars have finished (today) and"οι πόλεμοι τελείωσαν" the wars finished (in 1945). Or is the Greek as flexible as the English?
Yes, without further context, "έχουν τελειώσει" is fine as well. As far as the "today" example is concerned, you wouldn't use the Present Perfect in Greek, since it's about something that has come to an end, whereas it might be kind of debatable in English.