The e-mails were recently sent to university faculty members and students.
Officials said the fake e-mails came from a Google e-mail account, and they used search warrants to track down the person who sent them.
The university said evidence gathered by campus police led them to a current GVSU student, who admitted to sending the messages. University officials did not release the student's name.
Campus police will meet with the Ottawa County prosecutor's office for possible criminal charges. A judicial referral is being forwarded to the office of the dean of students for possible violation of the university's student code.