The Â£49m Pontio project was originally due to stage its first productions in September 2014, and the building schedule was blamed for the delays.
The October opening will be phased, with the full programme of events rolled out from December.
The new building will house the Bryn Terfel Theatre, research facilities and the students' union.
Earlier this year a construction worker described the project as "chaotic". Construction company Galliford Try accepted it had faced a number of challenges but that none were unusual for a project of this kind.
The centre's artistic director, Elen ap Robert, said: "We will be gradually trialling small scale shows, artistic events and screenings."
In a statement, the Arts Council of Wales welcomed the announcement, adding: "As people have watched this remarkable building take shape, they will have been intrigued by what might be available inside.
"Now local residents, artists and students will be able to see for themselves, touring the building and experiencing first hand this unique and innovative facility."
An arts and innovation centre will open at Bangor University in October, more than a year later than planned.