This is one of the most disputed topics in Byzantine history. The word ‘theme’ was originally used to describe an army unit and only later became a political subdivision, so it’s very difficult to distinguish which of the two the sources are referring to. Just to make things more confusing, the word “Theme” at first referred to military rolls, and the first Themes took the name of the army corps stationed there. It’s nearly impossible to say exactly when the name of a division became the name of an area. The one thing that everyone agrees on is that it happened during the Heraclid Dynasty, but the exact emperor is unknown. Generally Heraclius is credited (as part of his reorganization of the empire), but his son and grandson (Constantine III and Constans II) are also possibilities. One theory even has it that the last member of the family- the disastrous Justinian II- came up with it.
The primary sources seem to favor Heraclius. Theophanes the Confessor (8/9th C) mentions Heraclius arriving ‘in the land of the themes’, but this might be an example of attributing present day conditions to the past- like a Renaissance painting of a mythological scene that has everyone dressed in 15th Century clothes. The 10th Century emperor Constantine Porphyrogenitus wrote a book On Themes where he says that the Themes were ‘since the time of Heraclius the Libyan (African)’. So who developed the Theme system? This time I think common knowledge has it right. Probably (I follow professor Angeliki Laiou here) the first Themes were instituted by Herakleios and the full development of the system took time to mature.