The change of heart comes months after a lawsuit filed by the AIDS Law Project on behalf of the boy in November in U.S. District Court in Philadelphia, alleging that the school violated the Americans With Disabilities Act, which includes HIV.
The student, who is now 14 and lives in Delaware County where he attends public school, is considering the offer but is also looking at other options, said his lawyer, Ronda Goldfein.
"They said he was a threat to everybody. ... He has to do a lot of thinking about that," she said, adding that she was "delighted" the school reversed course but that they were pressing ahead with the case.
"We told them what the law was and they ignored it," Goldfein said. "They made some pretty negative comments about our client."
School spokeswoman Connie McNamara previously told ABC News that the school was worried the boy would have sex at some point at the school. Students live together in campus housing in groups of 10 to 12.
The school was founded by the chocolate magnate in 1909 for white male orphans and is now the nation's biggest and wealthiest boarding school for needy children of both sexes and all races.
Colistra said Hershey will no longer refuse admission to any qualified student who has HIV, and is issuing an equal opportunity policy to that effect. It is also developing training for staff and students on HIV issues, he said.
The president denied that the school did anything wrong by turning down the boy, noting that the "application of federal law to our unique residential setting was a novel and difficult issue."
The U.S. Department of Justice did not see it that way and advised the school that it "disagrees with how we evaluated the risks and applied the law," Colistra said.
"Our mission is to help children in need. It's who we are as members of the Milton Hershey School community. And it's what we have been doing for more than 100 years," said Colistra, a graduate of the school.
The school has been beset by a string of sexual scandals, including the sentencing last October of William Charney Jr., a married father of two who was responsible for residential life at the school and was a former house parent, for possessing almost 700 images and 40 videos of child pornography.
In 2010 the school settled the claims of five former students who said they had been sexually abused by a serial molester who gained access to the campus through his mother, a part-time house parent. And in 2007 and 2006, two teachers, one male and one female, were prosecuted in separate cases for having sexual relations with students.
A 2011 federal lawsuit described student sexual activity during a school-sponsored vacation to an amusement park in 2004. The then-vice president for residential life was said to have joked about the situation during a school social event.
Contact Kathy Boccella at 610-313-8123, firstname.lastname@example.org or @kmboccella on Twitter.