There is no such guide on the ridiculously convoluted method as it actually is on Android (WhatsApp's official guide is terrible and doesn't work), so here is mine:

1. Check if a chat backup happened in the last 24 hours; if not, have WhatsApp make a manual one
2. Go to Android/media/com.whatsapp/WhatsApp/Databases
3. Copy msgstore.db.crypt14 elsewhere

To restore:

1. Install WhatsApp on the new phone
2. Open the app, then back out of it immediately
3. Move the aforementioned msgstore.db.crypt14 copy to the step-2 folder above
4. Proceed while giving WhatsApp access to all permissions, including contacts (then deny them later if you'd like)