"The club is bigger than any one individual and Twente is too big in my heart to stand in the way of its progress," McClaren said in a statement on the club's website.
Twente's poor run has left them in fifth spot in the table, six points behind leaders PSV Eindhoven. Twente host second-placed Ajax Amsterdam on Saturday.
McClaren's departure brings to an end his second spell as manager at the club he guided to their maiden Dutch league title in 2010.
The 51-year-old Englishman returned to Twente in January 2012 after short periods in charge of German club VfL Wolfsburg and English second-tier outfit Nottingham Forest.
His decision to leave came after a meeting with the board following Saturday's 2-1 defeat by Heerenveen.
"We talked about the expectations of the club, how European qualification was key each season and finishing in the top four," he said.
"Despite being joint top at the winter break and second four weeks ago, recent results and performances have seen criticism, protest and demonstration from both supporters and the media.
"We talked about how we could change the situation and relieve the pressure on the team which was clearly affecting its performance."
He said he had sought assurances from the board about his position both now and in the future.
"After much discussion and deliberation those assurances weren't forthcoming and we have agreed it's in the best interest of the club that I leave."
The club have only 10 league games remaining to halt the slump and secure a top-four finish.
"We thought that the disappointing results under McClaren could be turned around," chairman Joop Munsterman said. "Steve, however, made clear that in the best interest of the team it would be better that he stepped down. We understand his decision and respect it."
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