Vatican ambassador to Kuala Lumpur, Joseph Marino, announced the appointment at a press conference on Thursday.
Father Leow takes over from Tan Sri Murphy Pakiam who stepped down as the third Catholic Archbishop of Kuala Lumpur after a 10-year tenure on Dec 14, 2013.
The appointment marked an especially ceremonious date for Father Leow as it fell on the Feast day of St Thomas the Apostle.
Father Leow, 50, was born in Seremban and ordained as a priest for the archdiocese of Kuala Lumpur on April 20, 2002.
Until his ordination as Archbishop, usually three months from today, Father Leow will retain his position as the Dean of Studies at College General Seminary in Penang.
Admitting that the appointment comes with a heavy responsibility, Father Leow nevertheless said that he will do his best with God's grace.
"I accepted the position in obedience, and after prayer," he said, adding that he was advised to receive the honour should it come by from a 'wise bishop' many months ago.
The archbishop-elect said that he "is looking forward to having inter-religious dialogues and fostering closer ties with Malaysians of various races and faiths."
"Once dialogue is shut out, there will be a lot of misinterpretation. Inter-religious dialogue is important for the whole country and we will find unity in diversity," he said.
On the use of the word Allah by the Christian community, Father Leow said that he will reserve comment until he has spoken with his lawyers.
"Every challenge can be looked upon as an opportunity," he said.
Pakiam vacated the seat after turning 75, the Church’s retirement age as prescribed by Canon law.
The Church has been without an archbishop for the past six months.
On Dec 21, Pakiam was elected Administrator of the Archdiocese of Kuala Lumpur.
In 2007, Pakiam filed for a judicial review to enable Christians to refer to their God as “Allah” after the Home Ministry banned the church’s weekly newspaper, The Herald, from usage of the word in its Bahasa Malaysian edition.