The Covenant House shelter, which is in the city's Kensington neighborhood, houses 20 formerly homeless people ages 18 to 21.
Many have aged out of the foster-care system or formerly lived on the streets.
The president of Covenant House said the shelter will provide a needed bridge to adulthood. Staff will help the clients set goals, while also teaching them life and housekeeping skills.
New Jersey native Bon Jovi is a longtime advocate for homeless auses in Philadelphia.
The Associated Press contributed to this report.