On Thursday, top Democrats said the legislation, blocked for more than a decade by Republicans, is "long overdue," arguing there is no justification for denying the undocumented immigrants a permanent home in the US.
They also said most of the immigrants the legislation will address have lived in the US for many years, with homes, businesses and US-born children and grandchildren.
The bill would also allow certain immigrants, who were previously deported, to apply to return to the US for humanitarian reasons.
In addition, some, including people brought to the country when they were children or so-called Dreamers as well as farmworkers, will be immediately proceeded to permanent residence or a "green card" meaning they can work legally.
Other immigrants are those who stayed in the country for years under temporary protected status (TPS) because of violent upheavals or natural disasters in their home countries.
The bill also proposes to stop branding undocumented immigrants as "aliens" in US law, and instead wants them to be called the less pejorative "non-citizens."
The bill underlines the Biden administration's reversal from former president Donald Trump's strident anti-immigration policies.