It comes despite calls from the Scottish Government to stay at home amid rising Covid-19 cases in the south of the city.
Police have called on fans to disperse with a significant police presence now in attendance.
Fans have travelled from as far as Northern Ireland for the occasion, with the Scottish Premiership trophy due to be lifted following today’s match against Aberdeen.
It’s the first time in 10 years that the club has taken a title.
A Greater Glasgow Police statement said: "Our operation ahead of the Rangers v Aberdeen match has started.
"Officers will be deploying at a number of locations including Ibrox Stadium and George Square.
"Supporters congregating should disperse, take personal responsibility and use Greater Glasgow safely and respectfully."
Footage circulating on social media showed a crowd of supporters welcoming manager Steven Gerrard as he arrived at Ibrox this morning, with the crowd quickly growing as more fans descended on the stadium to celebrate.
David Boardman, chairman of Randalstown Rangers Supporters Club, tweeted a picture of himself and fellow club members travelling to Glasgow from County Antrim this morning after setting off at 2am to catch an early morning ferry.
"There’s nothing stopping us from celebrating the 55,” Mr Boardman said. “It’s been a long time coming and it’s great for the younger fans to see.”
Further footage on social media showed a large number of Rangers fans on a plane from Belfast.
The Scottish Government earlier advised people to stay at home to celebrate Ranger’s winning the league.
Justice Secretary Humza Yousaf said fans had a “personal responsibility” to disperse given Covid-19 rates in the city.
Mr Yousaf tweeted: "While there is a significant Police presence at Ibrox and across City, this is ultimately about personal responsibility. If you have gathered you should disperse, particularly given yesterday's announcement about Covid in Glasgow.
"Yesterday, it was announced that lockdown restrictions would not be eased in the city given infection rates were now the highest in the country.”
Rangers have asked supporters to mark the club's title success in a "safe and sensible manner".
Large crowds had gathered at Ibrox in March when the title was secured.
Last night, the Clyde was lit up as over a hundred fans let off flares down by the water.
The display came not long after Rangers goalkeeper Allan McGregor was named the SPFL Player of the Year – with Steven Gerrard praising the player for his “magnificent” and “world class performances” at the club this year.
Rangers FC have added to the celebrations by releasing a much-awaited track by British rapper and composer Tinie Tempah created to mark the league win.
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