A student building monitor at Seattle Pacific University disarmed the gunman after he entered the foyer at Otto Miller Hall and several other students jumped on him and pinned him down until police arrived.
A 19-year-old man died at Harborview Medical Centre and three other people were taken to hospital, including a critically injured 20-year-old woman who underwent surgery.
Assistant police chief Paul McDonagh said the suspect in custody was a white man approximately 26 years of age who was not a student at the university in Washington state.
The afternoon shooting came a week before the end of the school year and the situation was particularly tense when police initially reported that they were searching for a second suspect.
They later said no one else was involved.