Purslow, a Liverpool season ticket holder, will work with Rafael Benitez on transfers, Phillip Nash on the club's finances and Ian Ayre on Club and commercial management.
"Tom and I felt that it was important to put a highly experienced and respected executive in place to run the Club and support the senior team and the Manager. There's a lot to get done over the summer to build on the great season we just had and Christian will be a valuable addition to the team," said Gillett.
"Christian has been a great supporter of the Club for many years and he's already built up good relationships at Anfield. His strategic and commercial acumen will be a real asset and we're delighted that he has made a long term commitment to the Club," added Hicks.