1965 Immigration and Nationality Act, a.k.a. the Hart-Celler Act (An Act to amend the Immigration and Nationality Act, and for other purposes)
H.R. 2580; Pub.L. 89-236; 79 Stat. 911.
89th Congress; October 3, 1965.
You can find the full text of this law as a PDF here.
The Hart-Celler Act abolished the national origins quota system that had structured American immigration policy since the 1920s, replacing it with a preference system that focused on immigrants' skills and family relationships with citizens or residents of the U.S. Numerical restrictions on visas were set at 170,000 per year, not including immediate relatives of U.S. citizens, nor "special immigrants" (including those born in "independent" nations in the Western hemisphere; former citizens; ministers; employees of the U.S. government abroad).
Effects of the Immigration Act of 1965 on Selected Population Characteristics of Immigrants to the United States - Journal article by Dr. Charles Keely: Demography vol.8 no.2, 1971.
"The 1965 Immigration Act" at Asian-Nation.org - An article that examines the origins and effects of the Act.
President Lyndon B. Johnson's Remarks at the Signing of the Immigration Bill, Liberty Island, New York October 3, 1965 - Full text of President Johnson's speech marking the passage of the Act.
1965 Immigration Law Changed the Face of America - Special report from NPR.org, with audio, text, and links to related stories.