As is the way with Animal Crossing titles

Animal Crossing BellsAnimal Crossing BellsAnimal Crossing Bells

Like with your own tent, and those of your first islanders, Tom Nook will provide you with Animal Crossing Bells a tent kit for Blathers. 

You'll need to head out into the world and find a space that you'd like for him - and eventually where the museum will sit.

As is the way with Animal Crossing titles, you can't rush anything. So in order forBlathers to arrive, you'll have to wait until the next real-world day.