The Irish Rugby Football Union revealed on Tuesday that they would not be offering Kidney a new contract, with his current deal due to expire at the end of June.
CEO Philip Browne said in a statement: "We would like to sincerely thank Declan for his commitment to Irish Rugby. His contribution and involvement across the spectrum of Irish rugby delivered Under Age, Provincial, Grand Slam and Triple Crown success, and epitomises his passion, belief and commitment to the game.
"With a host of new and emerging talent at every level, and despite the clear challenges ahead, we are confident of securing another world-class coach to work with this talented and ambitious group of players."
Interim head coach Les Kiss will now lead the team on their tour of North America.