She replaces Bishop Trevor Willmott, who retired from the post in May this year. The consecration took place in London on Tuesday ahead of her installation at Canterbury Cathedral on November 30.
“Beginning this new ministry, there is a sense of awe in it all,” she said.
“But also something refreshing about being open to the new things that God has in store – not just for me as a person taking on this new leadership role, but for our diocese as a whole.
“I’m excited – I’ve got lots of new people to meet, to get to know, and that fills me with joy.”
Bishop Hudson-Wilkin is the former Chaplain to the Speaker at the Houses of Parliament. The Bishop of Dover is the suffragan Bishop in the Diocese of Canterbury and holds additional delegated responsibilities for oversight of the diocese.
Welcoming her appointment into his diocese, Justin Welby, Archbishop of Canterbury, said: “When in October Rose stepped down as Chaplain to the Speaker, the tributes from all sides showed her pastoral, prophetic and faith sharing gifts.Even in times of division she was a point of unity and hope, to those of any or no faith. Through much struggle and suffering in her life she has become one of the most exceptional of Christian leaders showing, in word and deed, confidence in Jesus Christ as life, liberty and love.
“We welcome her, warmly confident that God who has led her this far will walk with her and speak through her.”
Bishop Hudson-Wilkin was consecrated alongside the Rt Rev Olivia Graham, who was made Bishop of Reading.
Archbishop of York, John Sentamu, delivered the sermon during their consecration.
He told them: “Be missionary Bishops who delight in God – and who are exposed daily to the vision of heaven and the tragedies of humankind. And loitering with intent at the intersection where the love of God in Jesus Christ and human need meet.
“When heaven touches earth, God-incidents happen.”