Intersport, which will run the event, announced the matchup on Thursday.
In August, Baylor coach Scott Drew told ESPN's Myron Medcalf the two teams planned to play at some point during the 2020-21 season.
"It's great for any sport whenever you can have potentially the top-two-ranked teams playing each other," Drew told ESPN at the time.
Baylor and Gonzaga also are two of the four teams scheduled to play in the Jimmy V Classic, but not against each other.
After guards Jared Butler and MaCio Teague withdrew their names from the NBA draft in early August, Baylor moved to the No. 1 spot in ESPN's Way-Too-Early Top 25. Gonzaga ended up dropping from No. 1 to No. 3 after Filip Petrusev signed a contract overseas and ended his college career. Coach Mark Few, however, received good news when Corey Kispert and Joel Ayayi decided to withdraw their names from the draft before the deadline.
There will be no fans in attendance for this game.