Welby, 69, announced his resignation in November after an independent inquiry found he had taken insufficient action to bring to justice one of the institution's worst abusers, a man who volunteered at Christian summer camps decades ago. The man, John Smyth, died in 2018.
Welby, head of the Church of England and leader of the 85 million Anglicans worldwide, said on resigning that he must take "personal and institutional responsibility" for a lack of action on the "heinous abuses".
Welby intends to complete his official duties by the Feast of Epiphany on Monday, his Lambeth Palace office said in a statement in November.
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The Church is also grappling with declining religious faith in Britain and internal divisions over how it approaches same-sex couples in its congregations.
A British Social Attitudes (BSA) report in 2019 said Britons were becoming steadily more secular, with just over one third of the public identifying as Christian. In 1983, when the BSA began measuring religious identity, that figure was 66 per cent.
Archbishop of York Stephen Cottrell, the Church's second most senior cleric, will take over Welby's official functions until Welby's successor is picked. That process could take six months.
Cottrell is himself facing scrutiny following a BBC report three weeks ago that said he had let a priest keep his job despite knowing the Church had barred him from being alone with children, and that he had paid compensation to a sexual abuse victim.
Cottrell has apologised for not having acted sooner on the case, saying he suspended the priest, David Tudor, at the first opportunity. The Church in October banned Tudor for life from ministry.
The Church's Christmas festivities were overshadowed by the scandals. Cottrell said in his Christmas Day sermon that the Church must "strip off her finery and kneel in penitence and adoration".
One of Welby's predecessors, George Carey, stepped down as a priest in December following allegations of mishandling Tudor's case.
"The current situation creates a worrying vulnerability for the Church," said Linda Woodhead, head of the Department of Theology and Religious Studies at King's College London. "The Church could soon find itself with no archbishop at the helm."
"This would create significant problems, even in the safeguarding realm, let alone other aspects of Church governance."
