Thirteen people were arrested following the Scotland v England world cup qualifier at Hampden on Saturday.
Police Scotland said the arrests were made in and around the ground.
The force had mounted largest single policing operation in its history to create a so-called ring of steel around the stadium in response to the terror attacks in London and Manchester.
The majority of fans behaved in a respectful manner and the “atmosphere was incredible”, police added.
The game ended in a 2-2 draw after England scored in stoppage time.
Ch Supt Brian McInulty said: “Thousands of fans visited Glasgow yesterday to help cheer on their national teams and throughout the day and night, the city centre was exceptionally busy, not just with football fans but with people out enjoying Glasgow’s busy social scene.
“The atmosphere was incredible with the large majority of supporters behaving in a respectful and responsible manner.”
Most of the arrests were for minor public order offences.
Some “isolated incidents” in the city centre, were dealt with swiftly, Ch Supt McInulty said.
He added: “A significant amount of planning and preparation was undertaken by the force and our partners with sufficient resources available to respond to any incidents.
“I believe that planning has paid off and the multi-agency operation has been extremely effective.”