The order will be completed on Monday, Mr Obama said, finishing a process begun during the administration of former president George Bush.
The United States is one of about a dozen countries that bars entry to travellers based on their HIV status. The ban has been in place for more than 20 years. Mr Obama said it will be lifted just after the new year, after a waiting period of about 60 days.
"If we want to be a global leader in combating HIV/Aids, we need to act like it," Mr Obama said at the White House before signing a bill to extend the Ryan White HIV/Aids program. Begun in 1990, the programme provides medical care, medication and support services to about half a million Americans with HIV or Aids, mostly low-income people.
In 1987, at a time of widespread fear and ignorance about HIV, the US health department added the virus to the list of communicable diseases that disqualified a person from entering the United States.
The department tried in 1991 to reverse its decision but was opposed by Congress, which in 1993 went the other way and made HIV infection the only medical condition explicitly listed under immigration law as grounds for inadmissibility to the country.
The law effectively has kept out thousands of students, tourists and refugees and complicated the adoption of children with HIV. No major international Aids conference has been held in the United States since 1993 because HIV-positive activists or researchers could not enter the country.
Mr Obama said lifting the ban "is a step that will save lives" by encouraging people to get tested and to get treatment.
Rachel B Tiven, executive director of Immigration Equality, said the ban pointlessly has barred people from the United States, and separated families with no benefit to public health.