St Johnstone and Police Scotland both confirmed that the restrictions, which were announced 48 hours earlier in a bid to prevent the use of pyrotechnics, had been lifted.
Celtic admitted jumping the gun with a statement on Monday following a major misunderstanding but, with the confusion over, they sent a clear message for their fans to behave in Perth.
Celtic's most recent Scottish Premiership away trip, against Motherwell, saw 18 smoke bombs let off, two of them thrown on to the pitch from the away fans, plus fireworks and a flare ignited. Celtic fans also broke more than 250 seats.
Their Boxing Day clash against Dundee at Dens Park last year also saw disturbances and they demanded a safe environment on Thursday.
A club statement read: "Football is about colour and atmosphere and creating a positive occasion for all and everything should be done to ensure that such an event can take place.
"However, we should also bear in mind that supporter safety is of paramount importance and we would re-iterate, therefore, that we do not welcome any form of pyrotechnics or smoke bombs at our matches.
"We want to see our matches played in a positive and safe atmosphere and we hope this will be the case on Boxing Day."
St Johnstone joined Celtic in asking police to lift the ban, which was initially instated because banners have been used as cover for pyrotechnics.
The Perth club said: "Both clubs have since received representations for their supporters on this matter and Celtic FC in particular has had extensive discussions with their main supporters' representatives and has been assured that their supporters will back their club in the right manner.
"Further discussion has today taken place between all parties and a request from the clubs made to Police Scotland that the ban be lifted has been accepted.
"Safety remains of paramount importance to both clubs and the match will be managed with this in mind and with Police Scotland having reviewed this policy, the two clubs are now putting their faith in all supporters that they shall support their respective teams in a manner which befits what should be a great game of football on a special date in the football calendar.
The match commander, Supt Kevin Lynch, added: ''Following further discussions with both football clubs and ourselves and having taken the views of supporters' associations into account, we support the decision taken by St Johnstone FC to allow flags and banners at this fixture.
''Police Scotland will continue to work with both clubs to ensure that everyone enjoys the game in true festive spirit in a safe and considerate manner."
Celtic manager Neil Lennon had earlier outlined his hopes for a positive atmosphere.
''One thing we want is the colour and atmosphere," he said. "What we don't want is the pyrotechnics, flares. It doesn't add anything to the game and it can affect people on and off the field.''