Dr Warner said he was “heartbroken” to be leaving his post in Whitby after two years as Bishop in the North Yorkshire town.
During his time in Yorkshire, he served the parishes of the Cleveland archdeaconry, including much of the North Yorkshire Moors and Middlesbrough.
“I am heart-broken to be leaving the North East so soon after arriving here.,” he said.
“The priests and people of the archdeaconry of Cleveland have taught me what it means to be a bishop.
They will remain in my affection and prayers as those for whose example and instruction I never cease to give thanks.”
Archbishop of York Dr John Sentamu praised Dr Warner for his commitment and described working with him as “great fun”.
Dr Warner , 53, succeeds Rt Rev John Hind, who has retired. He described his new position as “a daunting and exciting challenge”.
His appointment comes amid a troubling period in the diocese of Chichester, as it faces scrutiny over its child protection policies.
Earlier this year, the Church of England issued an apology for historic cases of child abuse by some of its clergy after it emerged that convicted paedophile Roy Cotton went on to be ordained as a priest in the diocese.
Two retired priests, Canon Gordon Rideout, 73, and Robert Coles, 70, were arrested in March on suspicion of sexually abusing children and young men. Both are on police bail pending further inquiries.