A 5-0 Ashes defeat raised questions over Flower's future earlier this winter, and the Zimbabwean believes that the decision to leave his role was required as England need a leader in charge of all three teams.
"Following the recent very disappointing Ashes defeat it is clear to me that this is now time for England cricket, led by Alastair Cook, to rebuild with a new set of values and goals," Flower said in a statement.
"The opportunity to start with a clean slate and begin to instil methods to ensure England cricket is moving in the right direction will be an incredibly exciting challenge for someone but I do not feel like I am in a position to undertake that challenge.
"In order for England cricket to make significant progress I believe that the team director, together with the respective captains, needs to be responsible across all formats in order to positively influence the rebuilding process.
Flower remains on the ECB selection committee and is expected to be given a role at the national academy in the near future.