Lennon had been shown a red card for arguing with the match officials after the final whistle following Celtic’s loss at Ibrox in August, before he pushed aside the assistant referee and then barged into Dougal.
Lennon received an automatic one-game ban for his initial red card and another two-game suspension was added “for misconduct of a significantly serious nature”.
Celtic said in a statement after the hearing: “We are satisfied with the process, today’s outcome and pleased that common sense has prevailed.”
Strachan had said after the incident that Celtic “wouldn’t be stupid enough to make a fool of ourselves by trying to defend things that are indefensible”, while Lennon publicly apologised for his behaviour.
Scottish Professional Footballers’ Association assistant secretary Fraser Wishart said Lennon’s previous good behaviour had worked in his favour.
Wishart said: “Neil wants to put this incident behind him and one of the stressing facts is that he has never been sent off in an SPL fixture or been over the top of the threshold for yellow cards.
“His previous record has been taken into consideration.”