Millions of undocumented migrants to the US will be given full legal status under sweeping immigration reforms due to be published on Tuesday by the Senate that will even include family members who have already been deported.

A summary of the bill, seen by the Guardian, is “surprisingly generous”, according to immigration experts who say it has the potential for transforming the lives of the estimated 11m people currently living in the legal shadows.

A further 400,000 people are deported each year, and about half of these –with no criminal convictions who are already out of the country – may also be eligible under an unexpected clause that may prove controversial among Republican activists in the House of Representatives.

But the bill, agreed by a bipartisan group of eight senators, is perhaps the most tangible consequence of President Obama’s second term-election win as Republican leaders have concluded they need to do more to reach out to voters in Latino and other minority groups.

Republican senators John McCain and Marco Rubio will be among those publishing the full bill later on Tuesday, although they chose to cancel a scheduled press conference following the explosions in Boston.

It follows weeks of backroom negotiations to square off conflicting interest groups such as labour unions and big business lobbyists, but the proposals retain much of the radicalism outlined by Obama when he first announced it as a second term priority.

Among the other key measures are:

• $1.5bn to look at fencing parts of the southern border with Mexico, possibly by the National Guard.

• A requirement that border security reaches 90% before legalisation begins.

• A new quota system for lower-skilled workers, particularly farmhands.

• The end of quotas for higher-skilled workers.

• Funding to speed up the 20-year backlog in family applications.

But by far the most significant impact will be for the millions of Latino and Asian families already living in the US, particularly the so-called “dreamers” – the foreign-born children of undocumented migrants who have grown up in the US but who currently lack legal status and can be deported at any time.

Edward Alden, an immigration expert at the Council on Foreign Relations, said: “The question is how many of these people will come forward as they have lived for years being scared of government. It looks like they will because the cut-off is quite generous: they only have to show they have been here since December 31, 2011.”

Those people previously deported before this date can also apply if they show they have close family members in the US and no criminal record.

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