The event, which is expected to attract some 50,000 fans, is normally policed by unarmed officers.
Chief Constable Phil Gormley said firearms officers would also be deployed at transport hubs and “crowded” places.
First Minister Nicola Sturgeon told MSPs there would be a full review of the cup final with the Scottish Football Association.
She said policing would be stepped up at other events such as at marathons, “VIP events” and in city centres.
The First Minister said security at every major event over the next two weeks would also be reviewed.
She said: There will be a significant increase in firearms officers on duty.”
There would also be an increase in the number of armed response vehicles deployed.
The Edinburgh Marathon and associated races, will involve some 30,000 participants this weekend, while former US president Barack Obama is due to speak at a dinner in the city on Friday.
Unarmed British Transport Police (BTP) patrols have also been stepped up at major railway stations.
Existing Police Scotland armed patrols at airport terminals have been increased in frequency as well.
A spokesman Network Rail said Glasgow Central Station, which is used by some 80,000 people a day, said: “There are a lot more police on the concourse than normal, for reassurance more than anything else.”
A spokesman for Edinburgh Airport, which handles nearly 40,000 passengers a day, said: “Police are more visible and they have upped both their armed and unarmed patrols.”
Mr Gormley said: “As part of the UK-wide response to these events, Police Scotland continues to review all safety and security plans and operations.
“This includes ensuring our armed policing and specialist resources are appropriately deployed.
“People will therefore see armed police on patrol at transport hubs and crowded places.
“There is no intelligence to suggest there is any threat to Scotland but I would ask the public to remain alert and report anything suspicious.”
BTP Assistant Chief Constable Robin Smith said: “Extra officers will be on patrol at key railway stations as well as on trains around the country.
“Throughout the day, commuters can expect to see additional officers on their journey.
“This will include both armed and unarmed officers.”