"We are delighted Christian has accepted our offer to help us and the club," said Tom Werner. "Liverpool will now begin a global search for a chief executive officer."
Purslow has said: "I came to Liverpool Football Club to oversee the sale process and get the best overall deal, including vitally the removal of the debt.
"I'm incredibly proud with what we've achieved and will assist the owners in any way I can at this exciting time as they drive the club forward to a bright future."
Purslow will remain as a non-executive director and adviser to the new owners.
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