At your option, FeedBurner now publishes directly to Twitter. All that you need to do is to allow Twitter to access your FeedBurner feed - from your blog, or from any other feed that you publish.
For any FeedBurner feed that you wish to publicise, go to the Publicize tab, and the Socialize menu entry.
Connect your feed to the real-time social web! With Socialize, FeedBurner will automatically post updates from your feed to your social media account.
Learn more about Socialize
If this is your first FeedBurner feed being Socialized, you'll have to hit the "Add a Twitter account" button, and login to Twitter and / or authorise your Twitter account to access your FeedBurner account.
With a Twitter account connected to FeedBurner, check and update your Formatting Options and Item Selection settings. Examine the Sample Item Preview, and decide whether the Preview provides a good example of your blog. Then, hit the Activate button, at the very bottom.
As an alternative to FeedBurner, you can use the third party TwitterFeed service, to publish to both FaceBook and Twitter.
Finally, get back to work publishing blog posts. And, enjoy the convenience of automated publishing to an additional blog service.