The two tracks - Under The Westway and The Puritan, written for the upcoming sold-out Hyde Park concert on August 12 - will be filmed and streamed live from a secret UK location.
Frontman Damon Albarn said -"I wrote these songs for Hyde Park and I'm really excited about getting out there and playing them for people."
Tony Wang, UK general manager, Twitter added: "People all over the world are connecting with the musicians they love on Twitter.
"Blur is taking this idea even further by debuting two new songs through a live stream and having a direct conversation with their fans on the platform. They know what their fans want and are setting the pace for the future of artist engagement online."
Fans can go to @blurofficial at 6:15pm to hear the first track and an exclusive band interview, followed by the second track at 7:15pm.
Following the live stream, both songs will be available to download. A limited edition double-A 7-inch single will be released by Parlophone on August 6.
Blur will perform a handful of warm up dates prior to the Hyde Park concert. The dates are:
August 1 Margate Winter Gardens
August 5/6 Wolverhampton Civic Hall
August 7 Plymouth Pavilions