In the near future we are to see a complete rework to the game's class system, which Riot covered the basics of in this blog. At the start of June, they published a thread in the Dev Corner that details the planned roles for each champions. For your convenience, I have combined below (left) a list of the planned classes as well as the champions Riot has assigned to them.
Note that Riot's is classifying champions by their target fantasy, rather than how they are currently played or built from patch-to-patch (e.g. Ekko's fantasy is an assassin, but he is currently played as a tank due to itemization exploitation). That said, in the comment section it has become apparent that Riot is defending a lot of their choices based on how the champion is currently played (e.g. Rek'Sai is listed as a Vanguard because she is currently built as a tank).
Overall - I find the new classes to have very weak distinctions. In the right column (below), I have implemented my own variation.