The first installment of the new franchise bows this summer, with production starting for the next film in the first quarter of next year. Release is set for May 2014.
Advanced buzz for the first film, which stars Andrew Garfield as the wall-climbing teen, has been strong.
"We grew up as huge Spider-Man fans so, to us, the opportunity to work on this film is akin to being handed the Holy Grail," Kurtzman and Orci said. "We love the direction Sony and the filmmakers are taking the Peter Parker/Spider-Man mythology, and we couldn't be more excited to be a part of this legendary franchise."
James Vanderbilt, whose credits include "The Rundown" and "Zodiac," penned the first draft.
Orci and Kurtzman have been collaborators for almost two decades, working together on projects such as "Transformers," "Star Trek" and "Cowboys & Aliens." Kurtzman is about to release his directorial debut, "People Like Us," this June.
"Alex and Bob have a unique ability to write great character and spectacular action that makes them pitch perfect for Spider-Man," producer Matt Tolmach said.
The trailer for the upcoming film can be seen at http://www.thewrap.com/movies/column-post/sony-asks-alex-kurtzman-roberto-orci-work-amazing-spiderman-sequel-37245.