Following a testing period, Microsoft has now rolled out Discord support for everyone on Xbox. Discord Voice is available across all Xbox Series X|S and Xbox One consoles today, September 13.
Anyone interested in taking advantage of the feature needs to first link your Discord account to your Xbox, even if you’ve linked accounts before.

Discord on Xbox will allow players to connect with friends–on Xbox, mobile, or PC–directly from the console. Presumably, Discord on Xbox may eventually allow users to chat to people on PlayStation, too, for supported cross-play titles. Players will be able to see who is on the call and speaking on Xbox. Additionally, players can switch between Discord and Xbox game chat whenever they want.