The force said they have taken action under section 12 of the Public Order Act in relation to the procession which was widely publicised on social media in the lead-up to today.
Police have the powers to use the legislation when they believe that conditions need to be imposed in order to ensure the safety of the wider public.
Police have issued a statement over an ongoing march involving Celtic fans from the Glasgow Green to Hampden Park ahead of the Scottish Cup final. https://www.glasgowtimes.co.uk/news/scottish-news/23565843.police-issue-statement-celtic-march-hampden-park/ #celtic #celticfc #glasgow #hampdenpark #scottish #scottishtiktok #fyp
♬ original sound - Glasgow Times
Police Scotland has imposed conditions under Section 12 of the Public Order Act 1986 on a procession, from Glasgow Green to Hampden Park, Glasgow today (Saturday, 3 June, 2023), on the grounds of public safety and to minimise disruption. More here: https://t.co/IJFrYRZMSY pic.twitter.com/xvTIWQT86Y
— Police Scotland Greater Glasgow (@PSOSGreaterGlas) June 3, 2023
In a statement published on social media, the force said: "Police Scotland has imposed conditions under Section 12 of the Public Order Act 1986 on a procession, from Glasgow Green to Hampden Park, Glasgow today on the grounds of public safety and to minimise disruption.
"Our priority is always public safety and this decision was taken after careful consideration of the potential impact on the local community."
The Glasgow Times contacted Police Scotland for more details on what conditions have been imposed using the power of this legalisation but was told by the force that they can say no more than the statement published on social media.
It comes after thousands of fans started gathering at the city centre park throughout this afternoon.
The main entrance of the park at Saltmarket is a direct route for fans to walk to the national stadium travelling along Crown Street onto Aitkenhead Road. The road is one of the busiest in the Southside and it is not known whether police will alter the route that Celtic fans had planned to take to minimise disruption to traffic.
We reported earlier that Hoops supporters planned a "meet and march" before the game today which will see them walk from the park to Hampden stadium.
The event is organised by the Green Brigade to celebrate the team's attempt to land the Treble.
It comes as Celtic and Inverness Caledonian Thistle will compete for the final piece of silverware this season.