I'm surprised no-one's mentioned his email to Mike Hearn on the 23rd of April 2011, where he said that he had "moved on to other things". It was a personal email, but it was the closest thing to a farewell he sent to anyone:
From: Satoshi Nakamoto [email protected]
Date: Sat, Apr 23, 2011 at 3:40 PM
To: Mike Hearn [email protected]
Subject: Re: Holding coins in an unspendable state for a rolling time window
I had a few other things on my mind (as always). One is, are you planning on rejoining the community at some point (eg for code reviews), or is your plan to permanently step back from the limelight?
I've moved on to other things. It's in good hands with Gavin and everyone.
I do hope your BitcoinJ continues to be developed into an alternative client. It gives Java devs something to work on, and it's easier with a simpler foundation that doesn't have to do everything. It'll get critical mass when impatient new users can get started using it while the other one is still downloading the block chain.
The only other email he sent after this date was one to Gavin Andresen on the 26th of April 2011, the day he is widely regarded to have "disappeared" (note that this email was quoted by Gavin in an interview):
I wish you wouldn’t keep talking about me as a mysterious shadowy figure, the press just turns that into a pirate currency angle. Maybe instead make it about the open source project and give more credit to your dev contributors; it helps motivate them.
Beyond this, there are two heavily disputed communications that may have occurred since 2011: The 2014 P2P foundation post, and the 2015 cryptography mailing list post. While never definitively disproven, these posts are regarded with high scepticism in the Bitcoin community (and rightfully so).