A swearing-in ceremony will be set later.
President Barack Obama nominated Brown in May for a judgeship presiding over court in Greenville, Miss. The post came open when U.S. District Judge W. Allen Pepper Jr. died in 2012.
Both of Mississippi's senators, Republicans Thad Cochran and Roger Wicker, supported Brown in the 90-0 confirmation vote Monday.
"I am confident Debra Brown will serve with distinction as a United States district court judge in Mississippi," Cochran told the Senate before the vote. "Her personal background, educational accomplishments, and legal experience should serve her well as she assumes this important position. The Senate vote is recognition of her qualifications to serve as a member of the federal judiciary."
Wicker said: "I am thrilled and honored to be part of this historic moment for Mississippi. Ms. Brown is a proven trailblazer. Our country needs judges who have a record of professional excellence, integrity, and public service. I am confident her service will be good for our nation, our state, and especially good for the city of Greenville, where she will preside."
Brown, who was born in 1963, is a Yazoo City native. She graduated with a bachelor's degree in architecture from Mississippi State University in 1987 and worked as an architect before going to law school. She earned a law degree from the University of Mississippi in 1997. She was a shareholder in the Jackson law firm Wise Carter Child & Caraway, which she joined in January 2012. Before that, she was a partner at the Jackson law firm Phelps Dunbar.
Wicker said it will be "particularly serendipitous" to have a trained architect as a federal judge in Greenville, because "the federal courthouse there is woefully inadequate and in desperate need of a new state-of-the-art courthouse."