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Purslow, a fluent Spanish speaker and Liverpool season ticket holder, will liaise with manager Rafael Benitez on his summer signings.
The 45-year-old will take overall charge until a replacement is found for outgoing chief executive Rick Parry.
George Gillett told the club's official website. "There's a lot to get done and Christian will be a valuable addition to the team."
Purslow is a Cambridge graduate with an MBA from Harvard Business School and Gillett said his experience was needed.
Purslow is an executive board member and co-founder of private equity firm MidOcean Partners.
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