Andersen took the Wisconsin job Thursday, taking over for Bret Bielema. Bielema left to take the Arkansas job.
Utah State president Stan Albrecht and athletic director Scott Barnes said hiring the 39-year-old Wells allows the football program to continue to build on the tremendous progress made by Andersen during the past four years.
"We're not starting over," Albrecht said. "This is not a step back. This is an amazingly wonderful step forward."
The 48-year-old Andersen just completed his fourth and best season at Utah State. The Aggies went 11-2, won the Western Athletic Conference and defeated Toledo on Saturday in the Famous Idaho Potato Bowl. They are expected to finish in the Top 25 in the final AP rankings.
It has been a remarkable rise for a program that had been near the bottom of major college football for years, and stuck in distant third in its own state behind BYU and Utah. The Aggies won nine games in the previous four seasons before Andersen took over. The last football coach to finish his tenure in Logan with a winning record was Phil Krueger, who went 21-12 from 1973-75.
Andersen drew interest from California, Colorado and Kentucky last month, but decided to pass on those opportunities and received a contract extension from Utah State. He said recently that he would stay, but changed course to take the Wisconsin job.
Wells said Thursday that he owes a lot to Andersen, who hired him two years ago. Andersen lobbied for him to get the job, he said.
"He's the guy that showed me the blueprint," Wells said about Andersen. "He's built this place with the help and support of the athletic department and administration."
He thanked Aggies players for making plays and winning games, giving him his first head coaching opportunity.
"If we would have stunk, Gary would still be here and I would have never gotten this chance," said Wells, laughing.
Barnes said Wells was his first choice even though he had a list of other candidates. The athletic director said they have no doubt they have a coach who can maintain the success the school had with Andersen.
"This program is bigger than any one person," Barnes said.
Wells said he'll build off the foundation established by Andersen. He said the Aggies will continue to play up tempo, spread offense and that he will stay with the same general defensive philosophy. He said his teams will compete for conference championships yearly.
Wells said he'll focus on hiring a staff and recruiting immediately. He said the Aggies' recent success has generated a lot of interest from coaches around the country. But he said anyone he hires will have to believe in his philosophy of how to treat players.
"We are going to coach them hard, and we are going love them hard," Wells said.
Wells played quarterback for the Aggies in the mid-1990s and graduated with a bachelor's degree in business marketing.
Prior to coming to Utah State, Wells coached at New Mexico, Louisville and Tulsa. He's from Sallisaw, Okla.
Wells becomes the 11th-youngest head coach in the NCAA's Football Bowl Subdivision, according to the Utah State sports information department. He's only the second Utah State graduate to come back and become head football coach.
With 16-of-22 starters returning next year, Wells said the Aggies should be very good again next year.
"I am extremely excited to get these guys on the field in the spring," Wells said.