The order will be finalized on Monday, Obama said, completing a process begun during the Bush administration.
The U.S. has been among a dozen countries that bar entry to travelers with visas or anyone seeking a green card based on their HIV status.
"If we want to be the global leader in combatting HIV/AIDS, we need to act like it," Obama said at the White House before signing a bill to extend the Ryan White HIV/AIDS program. Begun in 1990, the program provides medical care, medication and support services to about half a million people, most of them low-income.
The bill is named for an Indiana teenager who contracted AIDS through a blood transfusion at age 13. White went on to fight AIDS-related discrimination against him and others like him and help educate the country about the disease. He died in April 1990 at the age of 18.
His mother, Jeanne White-Ginder, attended the signing ceremony, as did several members of Congress and HIV/AIDS activists.
In 1987, at a time of widespread fear and ignorance about HIV, the Department of Health and Human Services added the disease to the list of communicable diseases that disqualified a person from entering the U.S.
The department tried in 1991 to reverse its decision but was opposed by Congress, which went the other way two years later and made HIV infection the only medical condition explicitly listed under immigration law as grounds for inadmissibility to the U.S.
The law effectively has kept out thousands of students, tourists and refugees and has complicated the adoption of children with HIV. No major international AIDS conference has been held in the U.S. since 1993, because HIV-positive activists and researchers cannot enter the country.
Obama said that by lifting the ban, the U.S. will take a step toward ending the stigma against people with HIV/AIDS, something he said has stopped people from getting tested and has helped spread the disease. More than 1 million people live with HIV/AIDS in the U.S., and more than 56,000 new infections are reported every year.
Obama noted his own effort several years ago to help combat the stigma. During a 2006 visit to Kenya, his father's native country, then-Sen. Obama and his wife, Michelle, publicly took an HIV/AIDS test.
The 11 other countries that ban HIV-positive travelers and immigrants are: Armenia, Brunei, Iraq, Libya, Moldova, Oman, Qatar, Russia, Saudi Arabia, South Korea and Sudan, according to the advocacy group Immigration Equality.
Several such groups welcomed Obama's announcement. Rachel B. Tiven, executive director of Immigration Equality, said the ban pointlessly has barred people from the U.S. and separated families with no benefit to public health.
"Now, those families can be reunited, and the United States can put its mouth where its money is: ending the stigma that perpetuates HIV transmission, supporting science and welcoming those who seek to build a life in this country," said Tiven, whose organization works for fairness in immigration for gay, lesbian, bisexual, transgender and HIV-positive people.