The Government’s intention is to have some people who have entered the UK illegally flown to the east African country to seek asylum there.
Senior Church of England bishops, including the archbishops of Canterbury and York, have criticised the plan for lacking morality.
A letter to The Times to be published on Tuesday, signed by the Most Rev Justin Welby and the Most Rev Stephen Cottrell, says: “Whether or not the first deportation flight leaves Britain today for Rwanda, this policy should shame us as a nation.”
It goes on: “The shame is our own, because our Christian heritage should inspire us to treat asylum seekers with compassion, fairness and justice, as we have for centuries.”
It reportedly goes on to say vulnerable people should be offered safe routes to the UK and not deported.
It adds: “This immoral policy shames Britain.”
The letter is also signed by the bishops of London, Durham, Exeter, Birmingham and Manchester.
Mr Welby had previously used his Easter sermon to say there were “serious ethical questions about sending asylum seekers overseas”.
He later said it would have been “cowardly” not to have spoken out against the plan.
Boris Johnson and other Cabinet ministers hit back at Mr Welby for his intervention in April.
Mr Johnson, according to sources who attended a private meeting between the Prime Minister and Tory MPs after Easter, claimed the senior clergyman had “misconstrued the policy”.
It comes after The Times and the Daily Mail reported that the Prince of Wales allegedly said in private that the policy is “appalling”.
Mr Johnson declined to comment on whether Charles was wrong in his comments, adding: “This is about making sure that we break the business model of criminal gangs who are not only risking people’s lives but undermining public confidence in legal migration.”
The Prime Minister’s official spokesman later said Mr Johnson “has nothing but respect and admiration for the Prince of Wales, who’s spoken out on a number of issues, not least the environment”.
A Government spokesperson said: “Our world-leading Partnership with Rwanda will see those making dangerous, unnecessary and illegal journeys to the UK relocated there to have their claims considered and rebuild their lives.
“There is no one single solution to the global migration crisis, but doing nothing is not an option and this partnership will help break the business model of criminal gangs and prevent loss of life.
“Rwanda is a fundamentally safe and secure country with a track record of supporting asylum seekers and we are confident the agreement is fully compliant with all national and international law.”