Great question. I think the oldest versions are papyri discovered in 1897 in Oxyrhynchus: https://en.wikipedia.org/wiki/Papyrus_Oxyrhynchus_18 https://en.wikipedia.org/wiki/Papyrus_Oxyrhynchus_19

although the text has been known continuously since antiquity, in various languages. Here’s a list of manuscripts: http://www.tertullian.org/rpearse/manuscripts/greek_classics.htm#Herodotus

Hopefully someone else knows more!