In the letter addressed to the "Trojan Community," Folt said Swann's resignation is effective immediately and called him "a leader on and off the field at USC for nearly five decades."
Folt, who was hired in March, said the fact that she's putting together a new leadership team at the university led to Swann's decision.
"He felt that this was the professional thing to do, to resign and allow me to build my team," Folt told the Los Angeles Times. "That really is the gist of it."
Folt told the Times the admissions scandal that rocked USC, as well as other schools, "was not a part of the decision for me."
Dave Roberts, a special adviser to Folt, will serve as the interim athletic director until a permanent replacement is found.
Roberts, who is also the vice chair of the NCAA committee on infractions, served as the vice president for athletics compliance at USC from 2010 to 2016, when he became a special adviser to then-president Max Nikias.
"The position will be filled with an experienced and accomplished individual," Folt wrote in the letter.
USC trustee Suzanne Nora Johnson, a former vice chairman at Goldman Sachs, will chair the search committee, which includes board of trustees chair Rick Caruso; trustees Jeff Smulyan and William McMorrow; alumni representative Bill Allen; vice president for student affairs Winston Crisp; faculty athletics representative Alan Green; academic senate president Rebecca Lonergan; and provost Charles Zukoski. It will also include two student representatives.
"Our Athletics Department puts our student-athletes first by pursuing excellence with integrity," Folt wrote. "We will build on the traditions and strengths of our exceptional athletics program.
"Our outstanding coaches, administrators and student-athletes work tirelessly every day both in the classroom and on the playing field, to embody the very best of the Trojan spirit. Our Athletics Department, working together with faculty and staff across the university, is focused on preparing all of our students for success in life, wherever they may go."
Swann was hired by USC in 2016, with the school naming the Pro Football Hall of Famer and Trojans great to replace Pat Haden.
During his tenure, Swann led the Trojans program to "five national championships in five different women's and men's sports" and "student-athletes' cumulative GPA for the past two years and our graduation rate of 86% last year were all-time highs for USC Athletics," Folt wrote.
But there were problems. The department was linked to multiple high-profile scandals, and the football program is coming off its first losing season (5-7) since 2000. (The Trojans are 2-0 this season.)
In January, former assistant basketball coach Tony Bland pleaded guilty to conspiracy to commit bribery by accepting cash payments to steer players to certain financial advisers and business managers.
And in March, multiple coaches and USC senior associate athletic director Donna Heinel were arrested for roles in the massive college admissions bribery scandal. One coach and one administrator admitted they took bribes to get students into the school. Both have pleaded guilty to racketeering conspiracy charges.
Roberts was asked by the Times about Clay Helton's future as the Trojans' football coach.
"I've known Clay since he's been here," Roberts told the Times. "He's a great guy. I think the world of him. We're going to do everything to put him in the best position to succeed. But he's a coach. He's going to stand on his record. President Folt and the new AD, they'll make that determination."
Swann, 67, graduated from USC in 1974 with a degree in public relations. He played in two Rose Bowls and won a national championship in 1972 before a nine-year Hall of Fame career in the NFL. He had a long career as a broadcaster for ABC and has served on several corporate boards.
Slovis throws 3 TDs in 1st USC start
Freshman QB Kedon Slovis throws for three touchdowns in USC's win vs. No. 23 Stanford.