The service should provide insight into online chatter about people, topics, brands and businesses.
Topsy, a social search and analytics startup, has created an index of all tweets ever posted dating back to March 2006.
The San Francisco-based company is gearing the service towards marketers, businesses and others to "extract meaningful signals from the social media noise."
The analytics firm said in a blog on its website: "Topsy APIs now offer the entire history of public tweets on Twitter, dating back to the first-ever tweet by Jack Dorsey in March 2006."
Topsy, which has 425 billion tweets including photos and links archived, said the service would provide insight into online chatter about people, topics, brands and businesses.
"To pull up your own early tweets, search for ‘from:yourusername’, select ‘All Time’ from the time range options on the left, then sort the results by oldest," Topsy explained
Twitter recently opened its Australian headquarters in Sydney as it seeks to boost its user base.