He succeeds Cardinal Vincent Nichols, who has held the role since 2009 and has stepped down aged 80.
For the past 10 years Richard Moth has been Bishop of Arundel and Brighton, and before that served as Bishop to the Forces.
As Archbishop of Westminster he will become president of the Bishops' Conference of England and Wales and lead an estimated six million Catholics.
Cardinal Nichols reached retirement age when he was 75, but was asked to stay on by Pope Francis. In May he took part in the conclave that elected Pope Leo XIV.
The search for a replacement for Cardinal Nichols was led by the Apostolic Nuncio, or papal ambassador to the UK, who presented a list of potential candidates to Pope Leo.
Earlier this week, Archbishop Moth released a joint statement calling for empathy for "those who come to this country for their safety", reminding Catholics that Jesus's family fled to Egypt as refugees.
He has been one of the bishops leading the Church's response to social justice issues in the UK, including praising the scrapping of the two-child benefit cap.
Archbishop Moth will face the challenge of declining numbers of people attending churches nationally, though there is growth in some churches with immigrant Catholics.
In response to the growing use of Christian symbols at, for example, rallies organised by the far-right activist Tommy Robinson, Bishop Moth has talked of his concern.
Last weekend, Robinson held an event in London saying he wanted to "reclaim" the country's heritage and Christian identity.
"We are concerned about the tensions that are growing in society and the desire by some groups to sow seeds of division within our communities. This does not reflect the spirit or message of Christmas," Bishop Moth said in a statement with the Archbishop of Birmingham.
The Catholic Church has been heavily involved in providing assistance to those who have suffered in the cost of living crisis.
As archbishop, Richard Moth will also lead the Church's constant challenge of dealing with safeguarding issues.
In 2020, a wide-ranging inquiry into child sexual abuse found that between 1970 and 2015 the Catholic Church in England and Wales received more than 3,000 complaints of child sexual abuse against more than 900 individuals connected to the Church.
In fact, the leadership of Archbishop Moth's predecessor, Cardinal Nichols, was criticised in the inquiry report, which said he cared more about the impact of abuse on the Church's reputation than on the victims.
At the time, Cardinal Nichols apologised and said he accepted the report, adding: "That so many suffered is a terrible shame with which I must live and from which I must learn."
Cardinal Nichols retires having led the Church in England and Wales for 16 years, during which it faced enormous change.
He is the son of two teachers and was born in Crosby. The lifelong Liverpool FC fan took up his first role as a priest in Wigan.
In 2010, he welcomed Pope Benedict XVI to England on an official visit.