Purslow left his post following the club's takeover by the company now known as Fenway Sports Group last October but had been retained as a special advisor and non-executive director.
Purslow was brought in by former owners Tom Hicks and George Gillett in 2009 and played a key role in negotiating the acrimonious sale of the Reds last year.
Crowded out: Purslow (centre), address the media outside London's High Court after Gillett and Hicks lost a legal bid to block Liverpool's sale
Purslow said: 'I have been happy to be available to provide support for the new owners during the transitional period since the sale but now Liverpool FC is in excellent shape for the future, and in safe hands, it is time for me to concentrate fully on other business interests.
'I look forward with pride and excitement to watching Liverpool FC compete at the highest levels once again.'
Purslow's exit follows that of former chairman Sir Martin Broughton, who left Anfield soon after the takeover.
New chairman Tom Werner said: 'We will always be grateful to Christian for his vital contribution to the club during his time as managing director and latterly as special advisor.
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Explore more:People: Tom Hicks, Martin Broughton, George Gillett Places: Liverpool