About 40,000 Aberdeen fans and 7,000 Inverness Caledonian Thistle supporters are expected to descend on Celtic Park for Sunday's showdown between the two sides.
Police Scotland Chief Superintendent Adrian Watson said spot checks would be carried out to ensure people were not carrying alcohol.
He said: "It is anticipated that Sunday will be a fantastic day for the north and north-east of Scotland.
"Police officers from Aberdeen will be working at the game supporting fans but also working closely with our colleagues in Glasgow, partner agencies, clubs, football authorities and the fans themselves to identify those determined to behave in an inappropriate manner.
"The relationship between Aberdeen and Inverness is very strong, and we expect the vast majority of fans to behave impeccably and to be a credit to the clubs they support."
Match commander Superintendent Mark Hargreaves said: "Police Scotland is delighted to welcome fans of both Aberdeen and Inverness Caledonian Thistle to Glasgow on Sunday for what is undoubtedly a momentous occasion for both teams and their supporters.
"I want to ensure that all fans enjoy their day at the match and I would urge everyone to do so in a safe and responsible manner."
An Aberdeen FC spokesman said: "This will be the biggest exodus of supporters from the north east to the central belt for many, many years and will be a fantastic family occasion with, fingers crossed, the right outcome.
"The vast majority of our fans behave impeccably at all matches and we're confident Sunday's final will be no different, and remembered as a great day out for the largest gathering of the Red Army for an extremely long time."
Alcohol will be banned on many train services before and after the match, and on-train patrols will be increased, police said.
Temporary Chief Superintendent John McBride, of British Transport Police, said: "Following reports of unruly and rowdy behaviour by fans on trains returning after the semi-finals, officers will take a dim view of anyone who flouts the alcohol restrictions put in place by ScotRail or indulges in anti-social behaviour, which is alcohol-fuelled or otherwise.
"Supporters need to remember that trains will be busy and not everyone will be going to watch the cup final. So, please bear this in mind and behave responsibly."
ScotRail has added five special trains from Aberdeen and Inverness to Glasgow to allow people to get to the match in time.