Fans congregated in Glasgow’s George Square and outside the city’s Ibrox Stadium after Rangers took their first top-flight title in ten years.
Police made 28 arrests and seven people were issued with fixed penalty notices or will be reported to the Procurator Fiscal.
Reasons for arrest included assaulting police officers, breaching coronavirus regulations, disorder, use of flares and sectarian breaches of the peace.
Deputy Chief Constable Malcolm Graham said: “The behaviour which we saw at the weekend was disgraceful and I utterly condemn the individuals who chose to completely disregard the coronavirus regulations, putting both the wider community and our officers at risk.
“I also strongly condemn the lack of support from Rangers Football Club over the messages we repeatedly asked them to put out to persuade fans not to go out celebrating and encourage those who did gather in large numbers to return home.
“We’ve been planning for the conclusion of the football season for some time since the league was allowed to resume and the sport is in a very privileged position given the restrictions seen across the country for almost a year.
“It was very clear through the lack of messaging that Rangers did not take seriously their responsibilities in terms of seeking to persuade their fans to celebrate safely and responsibly.”
He added: “I commend the officers who delivered a policing operation which was entirely consistent with our approach throughout this pandemic to maintain public safety and minimise disorder, disruption and damage to property.
“They did this faced with considerable danger, all of which was completely unnecessary and avoidable.
“Where large numbers of people gather at an unplanned event such as this, we use established crowd control measures to ensure we are keeping the public safe and manage those who are refusing to disperse.
“We will work with football clubs, local authorities and the Scottish Government to ensure we do everything we can to persuade people that none of these scenes can be repeated as the football season continues.”
It comes hours after Deputy First Minister John Swinney said the “silence from Rangers was deafening”.
Mr Swinney congratulated the club on their win and praised those who celebrated at home, but said the behaviour of some fans was an “absolute disgrace”.
He said: “To see so many people deliberately flouting (coronavirus) rules with no regard for the safety of others is shameful.
“Events like yesterday risk spreading the virus and they show no regard or respect at all for the millions of households across Scotland who have been sticking to the rules, who haven’t been able to meet up with friends and families to fully celebrate birthdays and other milestones or, in some cases, to attend funeral services of their loved ones.
“The Government and Police Scotland reminded Rangers of the need for the club to advise fans to adhere to the current restrictions in discussions on February 26 and March 5.
“It is a matter of profound regret that that did not happen.
“The Scottish Government will be making our extreme disappointment at the lack of leadership clear to the team management.”