Driscoll is well known to new Celtic manager Brendan Rodgers having worked with him at Liverpool and Swansea City.
Glen has also spent nine years at Chelsea where he worked with managers such as Jose Mourinho, Guus Hiddink and Carlo Ancelotti across the areas of performance, fitness and conditioning, physiotherapy and injury prevention.
Rodgers told the Celtic website: “Bringing Glen to Celtic is great news for our players who will benefit from the huge breadth of knowledge he has across all areas of performance.
“The experience he will bring to the club will be invaluable to our players and I know he will work very well with the excellent medical and performance staff already at the club.
“Performance, fitness, strength and conditioning, rehabilitation and injury prevention are all crucial elements in the modern game and we will be using Glen’s wide range of skills to ensure we achieve the highest standards across these areas.
“Glen’s talent in this area has been a massive support to me at both Liverpool and Swansea and I know he will deliver great work and great benefits to our players at Celtic.”
Glen added: “I am absolutely delighted to join Celtic, such an iconic name in world football and I am really looking forward to teaming up again with both Brendan and Chris.
“We have some highly talented elite players at the club and my role will be to ensure we give them all we can to achieve any extra edge possible.
“The areas I work in play a huge role ultimately in achieving maximum performance levels, in preventing injury and ensuring a high level of player availability.
“We are looking forward to meeting the squad in the next few weeks. Myself and the other performance staff at Celtic will work together and do all we can to help our players
achieve their own objectives as individual athletes and help the team as a whole deliver success to our fans.”