The Tigers lost their last two games against Exeter and Saracens to drop out of the playoff places and fall 15 points behind league leaders Wasps. They also suffered a record 38-0 European defeat by Munster last month.
"It is with great sadness and regret that I leave my position as director of rugby with immediate effect," Cockerill said in a statement on the club website.
"I still believe that I am the right person to lead the team at this present time but respect the Board's decision to make change as they see fit in the best interests of the club."
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Cockerill enjoyed two spells with the Tigers during his playing career, making over 250 appearances for the club before joining the backroom staff in 2004.
The former England hooker was appointed head coach in 2009 and director of rugby a year later, leading Leicester to a record 10th English top-flight title in 2013.
"This club has made me the person and the coach I am today," the 46-year-old added. "I will never forget what they have done for me."
(Reporting by Ed Dove, editing by Ed Osmond)
