Specialist officers have been drafted in and will work with local officers and match stewards at the Parkhead Club's Champions League fixture against Legia Warsaw.
And Police Scotland issued a booze warning ahead of tomorrow's crucial game.
Fans travelling to the match will be targeted to ensure they do not bring alcohol to the stadium.
Officers also vowed to crack down on supporters who have been drinking excessively or behave rowdily.
They warned travelling Celtic fans that "robust policing" would be in place.
Thousands of supporters are expected to travel to Poland from Glasgow Airport today and tomorrow.
A Police Scotland statement said: "We'll have officers there to help keep supporters safe.
"Supporters travelling to Warsaw remember - don't attend the stadium whilst under influence of alcohol, robust policing in place."
It is understood Scottish officers usually only make trips abroad for "high-profile" matches.
Legia's manager Henning Berg used to play for Celtic's Old Firm rivals Rangers.
The 44-year-old Norwegian played for the Ibrox side between 2003 and 2004, and made around 20 appearances.