Sources said the Prime Minister made the attack in a speech to Tory MPs after apologising over his coronavirus fine.
The criticism from Mr Johnson appeared to have come in a private address to Tory MPs in Parliament after he was forced to repeatedly apologise over the fine he received from police for breaching coronavirus laws.
Mr Welby raised “serious ethical questions” about the policy in his Easter Sunday address and said it cannot “stand the judgment of God”.
In the sermon, the archbishop said “sub-contracting out our responsibilities, even to a country that seeks to do well, like Rwanda, is the opposite of the nature of God who himself took responsibility for our failures”.
But sources said Mr Johnson accused “senior members of the clergy” of having “misconstrued the policy”.
The Prime Minister was said to have then added that the clergymen were “less vociferous” in their condemnation on Easter Sunday of Mr Putin than they were on the migration policy.
Though Mr Welby did not mention Russian president Vladimir Putin by name, he did call for a “Russian ceasefire, withdrawal and a commitment to talks”.
And he repeatedly criticised the invasion and discussed the plight of the Ukrainian people living through and fleeing the war.
Mr Johnson was met by the typical banging of tables and walls by Tory MPs during the speech in a Commons committee room on Tuesday evening.
Former prime minister Theresa May earlier said she does not support the policy of sending migrants who arrive by unauthorised means 4,000 miles to East Africa.
And she questioned the “legality, practicality and efficacy” of the widely-criticised plans.
But senior Tory Dame Andrea Leadsom criticised as “absolutely abhorrent and inexplicable” criticism from people like Mr Welby.
Enquanto isso, addressing the Prime Minister after his speech, the Tory MP for Colne Valley, Jason McCartney, was heard accusing Labour leader Sir Keir Starmer of a “whipping up of hysteria” and of using language that showed a “visceral hatred” of the Prime Minister.
Mr Johnson replied that there had been a “coarsening of the debate that does our politics no favours”.