By Alex Dobuzinskis

LOS ANGELES (Reuters) - California Governor Jerry Brown signed into law on Monday a bill allowing illegal immigrants to receive privately funded scholarships to attend the state's public colleges and universities.

The bill, dubbed the California Dream Act, passed the state Legislature earlier this month and aims at helping illegal immigrants who have earned a high school diploma after attending at least three years of high school in the state.

"At the end of the day, if we're going to continue as a powerful, equal-opportunity society, we're going to have to invest in our people," Brown, a Democrat, said at the signing ceremony in the library of a Los Angeles community college.

The state law is named after a national bill introduced in Congress last year to give young, undocumented immigrants who have lived in the United States for at least five years a path to citizenship through college or military service.

The federal bill failed to win passage in December 2010, and its chances have dimmed since a Republican majority took control of the House of Representatives this year.

Critics say the California Dream Act gives illegal immigrants a false promise, because their immigration status will not change after graduating from college, and they will remain unable to find legal employment.

The new law merely makes undocumented students who qualify eligible for private scholarships. Many are unable to otherwise afford more than a two-year degree from a community college.

A separate bill under consideration in the legislature would allow illegal immigrants to qualify for publicly funded scholarships as well.

State law already allows illegal immigrants in California who qualify for admission to a four-year state university to pay in-state tuition rather than the more expensive out-of-state tuition rate.

But four-year institutions are still beyond reach for many undocumented students without financial aid.

Twelve other states also grant in-state tuition eligibility to illegal immigrants based on attendance and graduation from a state high school, according to the National Conference of State Legislatures.

Arizona, Colorado, Georgia, South Carolina and Indiana bar illegal immigrants from in-state tuition benefits.

(Reporting by Alex Dobuzinskis; Editing by Steve Gorman and Jerry Norton and Todd Eastham)