56-year-old Hockaday was a shock appointment by the Italian on June 19 and now, ten weeks later, he has lost his job.
Hockaday - who listed Forest Green as his only managerial experience prior to taking the Leeds job - has lost four of his six competitive games in charge.
His end comes the day after a 2-1 defeat to Bradford City in the Capital One Cup and four days after Cellino backed out of a decision to sack him in the wake of a 4-1 defeat at Watford.
Cellino said at the weekend that he had chosen to blame himself and not Hockaday, but the man known in Italy as the 'manager eater' has now pulled the trigger for a third time since arriving in Yorkshire in January.
"I'd like to thank David for his efforts over the last two and a half months," Cellino said.
"But the results since the start of the season have meant we needed to act and make this decision.
"After the defeat at Bradford I realised that my decision to keep David at the club following the defeat at Watford was wrong, and I had to change my mind on the coach's position. As a club we will now begin our search for a new head coach."
Hockaday's assistant, Junior Lewis, has also lost his job and Neil Redfearn will lead the team against Bolton at Elland Road on Saturday.