The 6-foot guard will be eligible next season as a graduate transfer.
Webster shot 41.7% from the floor this season, hitting on 33.3% of his three-point attempts.
In his tweet, Webster said he couldn't pass up the opportunity to play for coach Fred Hoiberg due to Hoiberg's level of experience.
Webster said he met with Hoiberg and assistant Matt Abdelmassih last week "and I fully believe in their vision and the direction of the program."
The Cornhuskers went 7-25 this season, including a 2-18 mark in the Big Ten, in Hoiberg's first season with the program.