Before the events of inFamous, John is assigned by the NSA to infiltrate the First Son and collect information on Kessler. He does his best, leaving dead drops for his handlers to find in the city. On the day of the blast, John was trying to stop Cole from activating the Ray Sphere but missed him because of a red light.
John White appears assisting Cole in the last few missions of the game, after the Ray Sphere is destroyed/activated John is sucked into it and disappears. The alternate future version of The Beast is shown in Kessler's future vision of how he wrecked the world. This is the very reason Kesser travels back in time to fix this.
inFAMOUS 2The Beast is the main antagonist of inFamous 2. His true identity is revealed to be John White, whom Cole helped out in the first game trying to destroy the Ray Sphere. It turns out that the energy in the Ray Sphere took over John's body after he is sucked into a vortex of it. He literally pulls himself back together as Cole's boat is leaving for New Marais, and destroys Empire City. He then travels down the coast towards New Marais and reveals to Cole that he isn't commiting mass murder. He's activating Conduits in the cities he destroys, but killing all non-Conduits in the process.
In the canon (good) ending, The Beast is defeated when Cole uses the Ray Field Inhibitor, killing the Beast, himself and every other Conduit.
Cole joins The Beast and Kuo and works to awaken the conduits thus curing them of the plague. The Beast gets tired after Cole kills Nix and Zeke so The Beast gives Cole his powers and lets him complete the mission to awaken the conduits and cure them of the plague, while destroying all the life that does not have the conduit gene.
Possible discrepancy - A Second Beast?
Kessler's use of time-travel raises the question of whether John White was also the Beast of his original timeline. John White in the first game was transformed by events whose frame was shaped by Kessler's meddling in the new timeline. While it is possible the John White of the original timeline (if there was one, since Kessler had a century to alter known history) was the man who became the Beast through existing Ray Sphere experiments, the possibilities exist that the Beast of the original timeline was never (or has yet to be) transformed, or even that the original Beast could one day duplicate Kessler's one-way time door. These questions cannot be answered unless he appears in a new game emerges, if in fact any of these questions are part of its premise.