The Yorkshire club's owner Massimo Cellino has acted after Leeds lost 2-1 at local rivals Bradford City in the League Cup second round on Wednesday after conceding two late goals.
That loss followed Saturday's 4-1 thumping at Watford in the Championship which had increased the pressure on 56-year-old Hockaday, whose elevation from lowly Forest Green Rovers had caused consternation among Leeds fans.
"I'd like to thank David for his efforts over the last two and a half months but the results since the start of the season have meant we needed to act and make this decision," Cellino said on Twitter.
"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.”
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Neil Redfearn will take charge of the first team until a permanent replacement is appointed.
Leeds won the English title in 1992 but have struggled since their relegation from the Premier League a decade ago.
(Writing by Ken Ferris; Editing by Robert Woodward)
