You can upload photos to both Flickr and Twitter, or use the functionality to tweet about an already existing photograph. The system will automatically shorten the url using a "flic.kr" URL.
Getting started is simple enough and instructions can be found here.
The Flickr Blog has also provided us with a sample image of a tweeted photo:
This news must come as disconcerting to TwitPic, a website which allows the sharing of photos on Twitter. TwitPic seems to be the most widely used tool for photo sharing on the social networking giant, but this may not be the case in the near future.