The Parkhead side face Motherwell at Hampden on Saturday. If they win, the parade will take place that evening.
Celtic are aiming to become the first Scottish club to win back-to-back domestic trebles of league title, Scottish Cup and League Cup.
The parade announcement is something of a surprise. Unlike other clubs, Celtic and Rangers have tended to shy away from open-top bus parades on police advice.
However, Celtic have published details of the proposed route in the event of a victory in the final.
The procession would begin in the area around Dalmarnock Train Station at approximately 6:15pm, then travel along the Clyde Gateway, turn right on to London Road and then on to the Celtic Way.
If the final goes to extra-time and penalties, the start time of the procession would be delayed.
The club said in a statement: “Celtic Football Club is pleased today to outline its potential post-match plans for Saturday, providing important information to supporters, with the aim of assisting in planning.
“While we realise this will be an extremely difficult match against Motherwell (who are also putting in place similar post-match plans) and it will be a major challenge for Celtic to win this trophy once again, it has been decided that in the event of Celtic being successful in the Scottish Cup final, the club will stage an open-top bus procession on Saturday evening.”
Celtic were originally going to stage the parade on Sunday in conjunction with the Scott Brown Testimonial match against Republic of Ireland. However, it will now take place on the Saturday “following safety advice”.