The "Homes for Ukraine" programme will allow "tens of thousands" to gain access to work, healthcare and education, even without family ties to Britain, cabinet secretary Michael Gove said.
The government wanted to try to ensure that "every available home" is opened up "to those who are fleeing persecution", he told Sky News.
"There are a large number of people in this country, generous hearted and in a position to provide homes, and businesses and charities as well," added Gove, whose portfolio includes housing.
Hosts will be given £350 ($457, 418 euros) a month and must commit to a minimum stay of six months -- potentially a stumbling block when Britons are grappling with the worst cost-of-living crisis in a generation.
They must sponsor a named Ukrainian -- which Gove said could be someone Britons have met on social media, or with churches and charities playing an intermediary role.
Britons will need to undergo security vetting, especially to protect vulnerable women and children from Ukraine.
The refugees themselves will still require a visa, although the government has simplified the process after a deluge of attacks last week over the complications it had thrown up to fleeing Ukrainians.
Gove said that a website for Britons to register as sponsors would launch on Monday, with the first arrivals possible in a week.
The opposition Labour party welcomed the new scheme, but said the government still had to clarify key details and compared it unfavourably with the EU's no-strings approach to Ukrainian refugees.
"Frankly the last few weeks have been an embarrassment for the UK in terms of refugees," Labour leader Keir Starmer said on Sky.