They are the first sponsors approved under a new scheme unveiled by the Most Revd Justin Welby and the Home Secretary Amber Rudd at Lambeth Palace on Tuesday.
Churches and other community groups are being encouraged to help resettled families meet costs such as rent, clothing and baby equipment through the Full Community Sponsorship (FCS) programme.
The Archbishop said the UK has a history of helping the world's most vulnerable people and he also underlined the need for families to get the spiritual care they need regardless of their religion.
Speaking to Premier at the launch event, he said: "The sponsors, particularly those from within in the Church of England, will be seeking to ensure that they are properly cared for spiritually, as you would expected.
"It is the grace of God and the love of God poured out freely that is at the heart of this, not a calculation - on our part - of advantage.
"We have always had a history - it's one of the great facets of this country - of an effective and warm welcome for those fleeing foreign persecution.
"I have no doubt that deep-set nature of this country will rise to the surface."
Standing alongside the Most Revd Justin Welby, Amber Rudd underlined the government's commitment to resettling 20,000 Syrian refugees in the UK by the end of the current Parliament.
With more than 1,800 vulnerable Syrians so far given refuge in the UK, the home secretary admitted the pace of allowing fleeing families in will have to be increased.
She said meeting the Syrian family living at Lambeth Palace was a moving experience, adding: "I did ask, as one always, of the children, 'What do you want to do when you grow up?'
"All [four] children - aged four to ten - said: "We're going to be doctors."
"I'm really grateful to the Church of England for participating in [the scheme].
"I am really moved by the experience of meeting [the family] and hearing firsthand about what a really important and exciting change it is for them."
The government says each Syrian refugee arriving in the UK, including those involved in the FCS scheme, have gone through a two-stage vetting process.
Each family coming into the country will be allowed to stay for five years and, after this time, they can apply to extend their stay in the UK.