Great question — answering as the UphillTech team:
No exact date has been given yet other than "April 2019." Source: https://comicbook.com/anime/2019/01/19/fruits-basket-reboot-character-designs-additional-cast/
Full answer by Allison C: https://anime.stackexchange.com/a/50529 (CC BY-SA 4.0).
Need it done for your business? UphillTech.
Looking for somewhere to watch it on TV? Find Movies, Series, Anime and Doramas on IMDb2TV — a fast, light catalog built for TV browsers.