Napier averaged a team-best 17.1 points a game and earned a spot in the All-Big East first team. Connecticut went 20-10 on the season.
The deadline for underclassmen to declare eligibility for the NBA draft is Sunday.
"After many days of figuring out what decision was best for my family and me, I have decided to remain at UConn for my senior year," Napier said. "I am very much looking forward to getting closer to receiving my college degree, as well as becoming a stronger leader for my teammates on and off the court."
Napier enters his senior season at No. 31 on the all-time Connecticut scoring list with 1,239. He is 11th all-time in assists (451).