The 30-year-old striker was sent home from the Hoops training centre in Wales earlier in the month as police and the Parkhead club carried out investigations into his social media activity.
Police Scotland said it had established "no criminality" after carrying out a "full assessment" on claims Griffiths exchanged improper messages with a 15-year-old girl as well as another teen girl on social media.
Celtic boss Ange Postecoglou has now revealed he is back with the rest of the squad and will be available to play tomorrow evening.
Ahead of the visit of the Danish side, the Australian said: "He is ready to go. I think I said before the whole process with Leigh was pretty simple for me.
"Obviously with regard to the incident other people took control of that investigation and from what I understand everything has been sorted in terms of understanding what took place.
"From then he was made available and that's when he came back into my consciousness as a footballer.
"And I am not the kind who absolves himself of responsibility of things but with a limit of 24 hours every day and the amount if things I need to concentrate on, I decided that I will concentrate on the things I can control.
"And once Leigh came back into the squad and everything was settled in terms of the incident then he is back being a Celtic player, back as part of the squad and available for selection tomorrow."