Theresa May is to lay out the post-Brexit 'settled status' on offer for EU nationals resident in the UK.
David Davis said the plans will be laid out on Monday in a document roughly 15 pages long.
The Brexit Secretary said EU residents would "effectively" have the same rights as British citizens, and would be deported only if they had committed a crime or if there were security issues.
In an interview with the BBC, Davis insisted the offer would be fair.
He said: "They [EU nationals] get the same residency, employment, health, pension rights and so on - almost equivalent to British citizens.
"The only thing they don't get is the vote."
Theresa May's offer is subject to a reciprocal arrangement granting similar rights for UK citizens resident in the EU.
It received a mixed welcome from EU leaders last week.