It will replace Huron Hospital, which closed after 130 years.
The Cleveland Clinic closed Huron Hospital, citing financial issues.
Many people in the neighborhood questioned whether their health care needs could be met.
The new facility, named after the late Congresswoman Stephanie Tubbs Jones, is aimed at filling the void.
Tubbs Jones' sister, Barbara Walker, said, "It is a place to love, a place to help others, a place to heal."
Tubbs Jones' son, Mervyn, added, "This is a tremendous gift to the community. Something that if she had the willpower she would have done herself. My family thanks the Cleveland Clinic and everyone else who helped us grieve, helped us build and helped us move on."
The Stephanie Tubbs Jones Health Center will focus on the management of chronic diseases and shuttle patients to major hospitals when necessary.
Rep. Marcia Fudge, who replaced Tubbs Jones in Congress, said, "I look around and I see a health center that will go a long way toward addressing the needs of the people I represent, many of whom lack the resources that so many of us take for granted every day."
There will be an open house at the health center from noon to 4 p.m. on Saturday.
Stephanie Tubbs Jones died in 2008 from a ruptured brain aneurysm. She was 58 years old.