The Beachboys announced Search had stepped down on Sunday evening.
The move comes after a 2-0 loss to Bath City on Saturday - their third straight defeat in the Vanarama National League South.
After a promising start with back-to-back wins this season, their fortunes took a turn and Search leaves the club winless in 11 games.
A statement released on the Concord Rangers website indicated the club would be looking for a swift appointment.
It said: "Concord Rangers FC and Chris Search have today come to an agreement whereby Chris steps down as first team manager.
"We need to put on record that our club is extremely grateful to Chris, Danny Green, Craig Shipman, James Smith & Leigh Bailey for taking charge and helping stabilise a vital part of our club in one of the most challenging periods of our history.
"Searchy has put so much into our club in his time as manager, and has our clubs very best interests at heart.
"He has been a gentleman in his handling of this amicable parting and we are eager to continue a healthy relationship with him by opening the door to alternative opportunities for him to help drive our club forward.
"We will move quickly to appoint our new manager and will issue a statement on this development upon the close of our committee meeting scheduled for 19:30 Monday, 17 October."