A probe was launched on Monday after TikTok footage emerged of players and others singing inside an Ibrox function suite allegedly using offensive language.
Rangers declared themselves confident that no criminality had taken place, and said it was “deeply concerning” that the video had been “taken as genuine”.
In a statement released on Friday Police Scotland said: “In relation to a video circulating on social media showing Rangers players allegedly using sectarian language on Saturday 15 May, extensive enquiries have been carried out and no criminality has been established.”
After the video appeared online, then justice secretary Humza Yousaf said any player found to have been using sectarian language should be removed by Rangers.
On Monday he tweeted: “I have also been made aware of this clip, if (and I stress if) this clip is genuine then any player or staff member found to be guilty of anti-Catholic hatred should be shown the door by the Club.
“It is right Police Scot investigate & determine the facts around it.”
Thousands of supporters defied Covid-19 warnings against large gatherings and massed in Glasgow city centre last Saturday after the title win.
Five police officers were injured amid the disorder and 28 arrests were made at the time.
One off-duty police officer is among those fined for breaching coronavirus rules after he was spotted among the crowds at George Square.