Set in 1912, the game takes place on Columbia, a flying city in the sky that was originally designed to showcase America as an emerging world power.
After mysteriously disappearing for a number of years, former Pinkerton agent Booker DeWitt travels to Columbia to rescue Elizabeth, a young woman trapped on the city since childhood.
"We are excited to expand the world of BioShock, which is one of the industry's most critically-acclaimed and beloved franchises," said 2K president Christoph Hartmann.
"We believe that Irrational Games will lend their meticulous attention to detail and unique storytelling expertise to make BioShock Infinite an incredible entertainment experience that will immerse new and diehard fans of BioShock alike."
Creative director Ken Levine added: "In order to explore the floating city of Columbia, we needed an entirely new engine. To bring Elizabeth to life, we had to build brand new animation and AI systems.
"To create wide-ranging indoor and outdoor firefights at 30,000 feet, we had to rethink, rebuild and expand the BioShock arsenal. The only thing gamers can be certain of is this: the rules of the BioShock universe are about to change."
Developed by the studio that worked on the original BioShock, it will be released in 2012 for Xbox 360, PlayStation 3 and PC.
Click the 'play' button below to watch the announcement trailer.