The 44-year-old, who took over as coach from Simon Grayson in February 2013, met the board after Saturday's home defeat against Bournemouth and decided to part company.
"Mark has put his all into the job over the past 16 months and has made a big contribution to the Club," chairman Dean Hoyle said in a statement on the club's website (www.htafc.com).
"He arrived at the Club at a difficult time and immediately impacted to keep us in the Championship.
"Mark's approach to this has been refreshing. He has always put the Club before himself and worked tirelessly on the training ground to change our way of playing and we have seen that come to fruition.
"Mark will be someone that I personally, and we as a Club, will always remain in contact with."
Assistant manager Steve Thompson and first team coach Steve Eyre would take charge of training on Sunday, added the club, who finished 17th in the Championship last season.
(Writing by Sudipto Ganguly; Editing by John O'Brien)
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