Parkhead captain will join Stephen Glass as part of the new managerial team at Pittodrie.
Dermot Desmond says Peter Lawwell and Dominic McKay will both be involved in finding Neil Lennon's replacement.
Police Scotland confirmed that no arrests were made following the game which ended in a 1-1 draw between Rangers and Celtic.
Ibrox boss says supporters 'must stay safe' as Rangers prepare to travel across Glasgow to face Celtic next weekend.
Clubs told to send clear message to fans ahead of the Old Firm derby on March 21.
Lennon's departure comes after 1-0 defeat to bottom-placed Ross County on Sunday.
Parkhead club's half-year financial report shows revenues decreased by almost a quarter.
The Ivorian star missed training after the accident in the adverse weather.
Portuguese boss tells news conference he 'said no' to signing the French midfielder on loan from Celtic.
Lawwell will be succeeded by Scottish Rugby chief operating officer Dominic McKay.
Slovakian managed the Parkhead side during the 1998/99 season, which included 5-1 victory over Rangers.
Celtic captain believes a tenth consecutive Premiership title is still an achievable ambition for the Parkhead club.
Celtic boss says club didn't abuse any privilege and were 'totally professional' at their Middle East training camp.
Manager Neil Lennon says another player who is self-isolating following Dubai trip has Covid-19.
Club says all other players, management and members of backroom team have tested negative for coronavirus.
Croatian defender enjoyed a successful loan spell under both Brendan Rodgers and Neil Lennon in Glasgow.
First Minister believes Celtic have questions to answer over their trip to Dubai amid heightened coronavirus restrictions.
Parkhead club claim training camp was arranged months ago and was approved by all relevant authorities.
Celtic boss says his side in much better shape than in the weeks following their October defeat to Rangers.
Large crowd of demonstrators chant 'sack the board' ahead of club's Premiership clash against Kilmarnock.