Oregon formally announced Taggart's appointment Wednesday.
T.J. Weist, who won three games as UConn's interim coach after Paul Pasqualoni was fired in 2013, will coach South Florida in the Birmingham Bowl vs. South Carolina.
Taggart has led USF to an 18-7 record over the past two seasons, including a 10-2 mark this year. He also spent three seasons as coach of Western Kentucky, his alma mater, and was an assistant coach at Stanford under Jim Harbaugh.
Oregon fired Helfrich last week after the Ducks went 4-8. A news conference to formally introduce Taggart was set for Thursday.
"Oregon has a strong national presence and a proud recent history of playing among the nation's elite, and I look forward to the challenge of upholding the excellence," Taggart said in a statement. "I can't wait to get started."
Taggart, 40, is the first coach Oregon has hired from outside the program since 1976. The Ducks' previous three coaches, Mike Bellotti, Chip Kelly and Helfrich, were all assistants who were promoted.
Taggart will be the first black head football coach at Oregon. The length and terms of his contract with the Ducks were not immediately released.
Taggart was 16-20 at Western Kentucky, taking over when it was first transitioning to FBS. He went 7-5 in his last two seasons with the Hilltoppers and then moved to USF, not far from where he grew up in Bradenton, Florida.
It took two seasons and a change in offensive philosophy from more pro-style, West Coast schemes to a spread, but he now has the 25th-ranked Bulls rolling. They finished second in the American Athletic Conference East Division to Temple and will play South Carolina on Dec. 29 in the Birmingham Bowl.
Wednesday was the second straight day the AAC has lost one of its best coaches, and the third the conference has lost since Thanksgiving weekend. Temple's Matt Rhule was hired by Baylor on Monday and Tom Herman left Houston for Texas on Nov. 26.
Taggart had support from former NFL player and broadcaster Tony Dungy, whose son Eric played at USF in 2014 after transferring from Oregon.
Taggart served as running backs coach for Harbaugh at Stanford from 2007-09 and is credited with helping to recruit Andrew Luck. Harbaugh had recruited Taggart, a quarterback, to play at Western Kentucky under father Jack Harbaugh from 1995-98.
After taking over when Kelly left in 2013, Helfrich went 37-16 in his four seasons as head coach of the Ducks. He signed a contract extension in early 2015, and had an $11.6 million buyout.
Just two seasons ago, Oregon went to the first College Football Playoff championship game, led by Heisman Trophy-winning quarterback Marcus Mariota.
But the Ducks struggled this season with a five-game losing streak — the program's longest since 1996 — and finished at the bottom of the Pac-12 North with just two conference wins.
In a statement after his dismissal, Helfrich thanked his own family, the campus community, the fans, and his coaches and their families.
"Finally, to the players — thank you, and I love you," he said. "The future is bright for this young, talented team, and we will be supporting them and their new leadership."
Oregon athletic director Rob Mullens also reportedly interviewed Boise State's Bryan Harsin and Ohio State defensive coordinator Greg Schiano before settling on Taggart. Kelly, now with the San Francisco 49ers, had said he was not interested in the job, as did former offensive coordinator Scott Frost, now at Central Florida.
For the immediate future, Taggart will need to reach out to Oregon's recruits. Defensive back Deommodore Lenoir and defensive end Langi Tuifua both previously withdrew verbal commitments. Offensive lineman John Vaka said he was no longer committed via Twitter on Tuesday.