The Archbishop of York, Stephen Cottrell, says the Church must oppose racism "in all its forms".
His comments came in an address to a meeting of the General Synod over the weekend, days after the release of a major report from the Archbishop's Anti-Racism Taskforce challenging decades of inaction on racism despite successive reports and recommendations over the years.
Among the 47 recommendations in the report are the appointment of full-time diocesan racial justice officers, and shortlists for senior clergy appointments that include at least one minority ethnic candidate.
In his presidential address to Synod, Archbishop Cottrell said he had been on a "long journey of learning" as "a privileged white man".
He reiterated that "racism is a sin" and said it "must be confronted with a call to repentance and with the healing, reconciling promise of the gospel".
"When George Floyd was murdered last year his last words were: I cannot breathe," he said.
"Those words echoed around the world, summing up so many peoples experience of not having the space to be themselves, of being second-class citizens in someone else's world.
"This is the antithesis of the belonging and the new humanity we have in Christ that the Christian faith declares.
"It is, therefore, a gospel imperative for the Church of Jesus Christ to oppose racism in all its forms, to prophetically call for racial justice, and to challenge the white hegemony which so often still controls the narratives of the world."
The taskforce's report was released three days after the airing of a BBC Panorama documentary featuring black and minority ethnic clergy who disclosed shocking accounts of racism and accused the Church of using non-disclosure agreements (NDAs) against them when they complained.
After the programme aired, the Archbishop of Canterbury, Justin Welby, told Times Radio he was "horrified" by the use of NDAs.
Addressing the allegations on Panorama, Archbishop Cottrell said they were "sobering and shameful for the Church of England".
"With Archbishop Justin, I want to emphasise our immediate response to the programme, which is that non-disclosure agreements should not be used except in the most exceptional of circumstances, and then only to protect the victim, not the reputation of the institution," he told Synod.
"We are sorry that this has not always been the case."
The Archbishop went on to say that he could not "defend our record" on racism, and that he could not promise "everything will be ok" unless the Church takes urgent action.
"I'm saying that there is racism in the Church and it must be confronted. But no longer by words. We have to do something. We have to become the change we long to see," he said.
He continued, "The Church of England owes some of our sisters and brothers in Christ a much greater apology than this; and for much greater wrongs.
"But most of all we owe it to the nation we serve and to the God we love, that in this watershed moment – the week when George Floyd's killer was brought to justice - we will now commit ourselves to change.
"For any of my own failings in this I am truly sorry. But let me remind you: one of our named strategic objectives is to be a diverse church. I'm determined to make that happen.Because it is a gospel issue. Because it is the theological vision of our belonging to one another in Christ that drives our mission. Because we all need to breathe.
"And because our facing this issue of racial justice is itself a movement of the Spirit breathing God's life of unity and glorious God given diversity into God's Church."