Good question.
Assuming you purchased from Disney rather than resale: they don't bother telling you when you have closed.
You can do two things:
a) Go to the Orange County Comptroller website and see if your deed has been recorded.
http://www.occompt.com/
click on "Records Search" on the right.
You are looking for your name as Grantee.
This won't tell you when you closed, but obviously if the deed was recorded, you have closed.
b) Call Member Administration and ask them if you have closed.
800-********
I believe you then press 2
They are open Monday through Friday, 9:00 am - 5:00 pm Eastern time
Member Administration told me that after the deed is recorded, it is sent back to Disney. Disney then issues a title policy and sends it to you with the deed. It can take several weeks.
I FedExed my paperwork back to Disney on 08/31, closing was on 09/10, deed was recorded on 09/16. I have not received the deed as of today (09/21). Labor Day fell in the middle of all this.
You would think that they would at least send you a postcard letting you know that the transaction closed - but no.