Interesting news, for several reasons. First, of course, DePodesta is part of the "new wave" of stat-minded general managers, and one of the main characters in Moneyball. New Dodger owner Frank McCourt gave DePodesta a sizeable five year contract to lure him away from the Oakland A's.
However, DePodesta appears to have lost a power struggle with former L.A. manager and "senior advisor" Tommy Lasorda, who seems to have opposed DePodesta from the outset, and who appears to have gotten the ear of McCourt.
From the way it sounds in the press, DePodesta was on the verge of hiring Terry Collins as the team's new manager. But Lasorda and McCourt had dinner with Orel Hershiser (the popular choice in L.A. to take over as manager), while DePodesta had only a telephone interview with him. It looks like DePodesta's brush-off of Hershiser as a managerial candidate was what gave Lasorda the opportunity to drive the final wedge between DePodesta and McCourt, and force DePodesta out.
My guess is that Hershiser gets hired as manager in a matter of days, with either Lasorda taking over as general manager, or Lasorda hand-picking the new g.m.
As for the impact on the Rangers, my guess would be that Mark Conners would take over as pitching coach, with John Wetteland likely assuming the role of bullpen coach.