The Scotland forward, 28, will begin”fitness and performance work” together with medical staff with a view to coming to complete training”from the future”.
Celtic director Neil Lennon said that there is”no timescale” on a come back to first-team actions for its striker.
“I would love to thank every one for showing me like support,” Griffiths said.
“I am so grateful to the club for whatever they have given me and also the manner by which they have supported me strongly.”
There is speculation he had difficulties with betting, but that the striker said which was”ridiculous”, hinting he was absent for mental health reasons.
Lennon, who said 10 days he expected to own back the player before the end of the season, said he was”really pleased” with his own reunite.
“We are able to make sure we work together with him to the most effective, most productive way forward,” he added. “We will not rush him whatsoever and we will allow him to carry things at the pace he is confident with.
“We will continue to offer Leigh every support to be certain his health and wellbeing are our number 1 priority.”
Griffiths had made 2-2 Celtic looks – scoring six objects – in an effort which had been disrupted with injuries.