Justin Welby will instead spend the festive period privately with his family, after announcing in November that he would resign over the Church's handling of one of its worst-ever abuse scandals, Lambeth Palace said.
The Church confirmed this week that the archbishop's former chaplain had "stepped back" from her current role as a bishop following the publication of a damning report into the scandal.
Mr Welby intends to complete all official duties as archbishop by 6 January.
The BBC had already confirmed he would not deliver the traditional televised message on New Year's Day.
The archbishop's Christmas Day sermon from Canterbury Cathedral has been a longstanding Church of England tradition.
With Mr Welby missing the service, Archbishop of York Stephen Cottrell's Christmas sermon is likely to be the Church's focus instead.
As the second-most senior bishop in the Church of England, Mr Cottrell is expected to take over the Archbishop of Canterbury's official functions on a temporary basis after 6 January.
A timeframe for appointing Mr Welby's replacement has not been announced, but the process is likely to take around six months. Mr Cottrell appears to have ruled himself out as a candidate.
Mr Welby announced his resignation in November, after the independent Makin report found that he "could and should" have reported child abuser John Smyth to the police in 2013.
Smyth is believed to be one of the most prolific abusers associated with the Church, attacking more than 100 boys and young men at Christian summer camps in England in the 1970s and 1980s, and later in southern Africa.
He is thought to have continued his abuse in South Africa until he died in Cape Town in 2018, aged 75.
The report said "several opportunities were missed" to formally report the abuse to police, and named Mr Welby specifically as someone who knew about Smyth's behaviour.
In his resignation statement, the archbishop said "it is very clear that I must take personal and institutional responsibility" for his response after he was first told about the abuse.
"I believe that stepping aside is in the best interests of the Church of England," he added. "As I step down I do so in sorrow with all victims and survivors of abuse."
Rev Jo Bailey Wells, Mr Welby's former personal chaplain, stepped back from her ministry following the publication of the Makin report, the Diocese of London said this week.
In the wake of the archbishop's resignation, several Anglican leaders stressed the importance of improving safeguarding measures in the Church.
Some survivors of Smyth's abuse welcomed Mr Welby's decision, but some said others who were involved in what the archbishop himself called a "conspiracy of silence" around Smyth should also resign.
An announcement earlier this week confirmed the Rev Jo Bailey Wells, the archbishop's former personal chaplain, had "stepped back from her ministry" following the independent review.
A Diocese of London spokesperson said a safeguarding risk assessment would take place.
On Sunday, the Bishop of Newcastle, Helen-Ann Hartley, told the BBC she had been "frozen out" by her Church of England colleagues after she became the most senior member of the clergy to publicly call for Mr Welby's resignation.
The Church of England said: "The national safeguarding team is considering whether there was any new information in the Makin report that needs to be assessed for any ongoing safeguarding risk and any evidence to support any disciplinary or capability process against individuals named in the report who are still under the authority or oversight of the [Church]."