The Scottish Government announced on Tuesday that organisers of outdoor events would still need to apply to local authorities for permission to host more than 5,000 spectators, when Scotland moves out of the vast majority of coronavirus restrictions from August 9.
But Celtic and Rangers have already received good news from Glasgow's Safety Advisory Group, which is composed of city council officials, building regulators and representatives from the emergency services.
A Celtic statement read: "We are delighted to announce that we have received confirmation from the local Safety Advisory Group that following Tuesday's Scottish Government announcement and positive reviews of recent matches and associated protocols, full capacity crowds will now be permitted at Celtic Park from Monday, August 9 onwards.
"We have been working relentlessly behind the scenes to bring our supporters back, and we are thrilled to finally be able to make this announcement."
Celtic chief executive Dom McKay added: "I would like to thank our fans for all the fantastic support they have given us in reaching these levels. I would especially like to thank our staff for their tireless efforts and hard work in getting us to this stage.
"Our team have been a leading force in Scottish sport, writing and exercising protocols and procedures to allow us to return to train and play.
"Now, through their hard work and leadership, we are finally welcoming you, our fans, back where you belong. I must also thank the Scottish Government, Glasgow City Council and the Safety Advisory Group for all their co-operation."
Rangers had earlier confirmed there would be a full capacity at Ibrox going forward, "subject to conditions prescribed by the Safety Advisory Group of Glasgow City Council".
Ibrox hosted 23,000 fans for the cinch Premiership opener while 24,500 will be inside Celtic Park when Dundee visit the east end of Glasgow on Sunday.
Both clubs will be able to welcome a full house when they play the second legs of their European ties next week.
Other Premiership clubs will also have to secure approval from their local authorities.
Aberdeen have submitted an application for full capacity for their home games for the rest of the season after being allowed 6,305 fans against Dundee United on Sunday.
Chairman Dave Cormack added he was "hopeful of a positive decision" on Friday afternoon ahead of their home European game against Breidablik next week.
St Johnstone have also been in discussions with Perth and Kinross Council officials ahead of their return leg against Galatasaray next Thursday.