Former Prime Minister, David Cameron announced the plans to be led by the UK Holocaust Memorial Foundation in 2016, but the proposals have received criticism from conservation groups that argue the centre would harm the area's parliamentary heritage.
The application by Adjaye Associates and Ron Arad Architects, proposes a series of bronze structures to be built on Victoria Gardens, together with an underground learning centre to commemorate the six million Jews murdered during the Second World War.
In a letter to the Westminster Council, Mr Welby highlighted the importance of preserving the "memory of the thin line which distinguishes us from the atrocities of the past."
"Memory comes from experience and education. Experience is deepened by symbolism. The symbolism of this centre, right next to the home of our democracy is profound and hugely powerful."
He added: "I believe it will add significantly to the status of the City of Westminster as a place of government that is a world model. I do hope that these factors will be taken into account."
This comes after the application prompted a number of anti-Semitic comments online, with some members of the public claiming Jews are given "special privileges" and that the project was "discriminatory and racist" to white British war victims.
Together with Mr Welby, national faith leaders of the Jewish, Catholic and Muslim communities have written to Westminster City Council, offering their support for the development.
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