Kent and another U.S. national, Nancy Writebol, were working with aid group Samaritan's Purse to treat Ebola patients when they were both diagnosed with the virus last week.
Brantly, of Fort Worth, Texas, arrived on a charter plane Saturday at Dobbins Air Reserve Base near Atlanta. He was transported to Emory University Hospital in Atlanta for treatment.
The hospital is situated near the headquarters for the U.S. Centers for Disease Control.
Todd Shearer, a spokesman for Samaritan's Purse, said it is hoped Writebol will be brought to the United States early next week.
Brantly's wife, Amber Brantly, issued a statement giving thanks for the support her family has received throughout her husband's illness.
"I remain hopeful and believing that Kent will be healed from this dreadful disease," she said.
"I have been encouraged by the Writebol family and their bravery during this situation. They have kindly reached out to me and offered their full support and prayers as we walk this road together," Amber Brantly added. "I ask for your continued prayers for Kent, Nancy, and the many others who are suffering."
The symptoms of the Ebola virus, also known as Ebola hemorrhagic fever, include fever, headache, joint and muscle aches, weakness, diarrhea, vomiting, stomach pain, lack of appetite, and bleeding inside and outside the body, the CDC said.
The World Health Organization estimates some 1,323 people in Guinea, Liberia, Nigeria and Sierra Leone have contracted the virus with 729 suspected deaths.
There have been 909 confirmed cases with 485 known deaths.