While Israeli Jews are required to do military service, people with HIV have long been exempt on medical grounds.
The Israel Defence Forces (IDF) confirmed this policy would be scrapped in the coming months.
However, HIV-positive soldiers will not serve in combat roles but in administrative and other positions.
Colonel Moshe Pinkert, head of the IDF's medical services department, said new treatments meant the risk of HIV-positive citizens passing the disease on was limited.
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The announcement, made to coincide with World Aids Day on December 1, was hailed by gay rights groups.
"This process is a significant step towards shattering stereotypes about people with HIV," Yuval Livnat, CEO of the Israel Aids Task Force, said in a statement.
Israel's government has long trumpeted its military's gay-friendly stance.
The army was among the first around the globe to provide benefits to the partners of deceased gay soldiers.
A pro-Palestinian gay campaign group, Pinkwatching Israel, has accused the IDF of seeking to use its stance to divert attention away from alleged Israeli abuses against Palestinians, describing it as "pinkwashing".