Original announcement from the Rockstar Twitter.
Update 11/2: Trailer released on Rockstar's website and YouTube.
Update 11/3: Official announcement from the Rockstar website:
Update 7/12: Two new GTA:V screens."We are very proud to officially announce that Grand Theft Auto V is in full development.
Developed by series creator Rockstar North, Grand Theft Auto V heads to the city of Los Santos and surrounding hills, countryside and beaches in the largest and most ambitious game Rockstar has yet created.
A bold new direction in open-world freedom, storytelling, mission-based gameplay and online multiplayer, Grand Theft Auto V focuses on the pursuit of the almighty dollar in a re-imagined, present day Southern California."
Update 10/30: GTA:V officially set to release "Spring" 2013
Update 11/8: GTA:V Game Informer Cover Article detailing many of the specifics.
Update 11/14: Trailer #2
Update 1/31: GTA:V release date delayed to 9/17/2013
Update 4/30: Character trailers
Update 5/2: Worldwide GTA:V Preview. Lots of information and screens here.
Update 7/10: Official Gameplay Video
Update 8/15: GTA Online Reveal
More updates to follow!