Update 19/05: AMD later clarified some new plans but they come with plenty of caveats.
If you're keeping an eye on the latest AMD processors coming, you might want to sit down and take a look at a recent post from AMD detailing their support plans for socket AM4 and Zen 3 compatibility.
Writing in a post on their community forum, AMD developer Robert Hallock announced their plans. Going over a little history, how in 2016 they said they would support socket AM4 until 2020 and since then processors have expanded a lot across the Excavator / Zen / Zen+ and Zen 2 architectures.
Starting off with the big question answered: the upcoming Zen 3 will be compatible with the X570 (2019) and B550 (2020) motherboards through a BIOS update. While they also mentioned "no plans" to have Zen 3 support older chipsets so if you were waiting on it you're likely going to need to spend more.
They've also provided a picture of their support status and plan:
For the full details, see here.
Curious about their upcoming Zen 3? AMD stated recently that it and their next-generation GPU architecture with RDNA 2 are on target for this year.