Yes! The moment which you have been waiting for is finally available. Twitter has enabled the option to download all your tweets in a calendar type archive. The option is working only for few accounts at the moment. Seems it will be rolled out gradually. Go to your settings page and check if you see something like the following

Twitter Archive Option

On clicking this, twitter informs that they will mail you the download link when the archive is ready. Yes, its just like how Facebook’s archive system works. Once you get the mail and download it you will get a zip file with archive in html form. Extracting it and you will see all your tweets sorted in calendar format.

Twitter Web Archive

Some people are saying that few tweets are missing from the archive. Either Twitter is testing the feature or waiting to roll it out. Till now no official announcement has been made.

Thanks to @Psilosophy for reporting it.