Two men have been arrested outside the stadium where the Old Firm game took place on Sunday.
Celtic beat Rangers 4-0 in the Scottish Cup semi-final at Hampden Park in Glasgow.
Police said that a 63-year-old man was arrested and charged in connection with an alleged sectarian breach of the peace.
He will be released on an undertaking to appear at court at a later date.
Celtic 4 Rangers 0: Hoops steamroll their way past Rangers and into Scottish Cup final
A 21-year-old man has been arrested in connection with alleged culpable and reckless conduct over the use of pyrotechnics.
He will be reported to the Procurator Fiscal, police said.
Celtic will play Motherwell in the William Hill Scottish Cup final at Hampden Park on May 19.
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