Liverpool-born Moore, a passionate Reds fan, joins the club from Electronic Arts where he held the position of chief competition officer as well as a number of leadership positions in his decade with the gaming industry giant.
"I am not only incredibly proud to be joining a club that I have held very close to my heart my whole life, but also extremely determined to give everything I have to bring success to Anfield," he told Liverpoolfc.com.
"To be charged with the task of leading this incredible institution is a huge honour and I hope to be able to build upon the successes of my predecessor and use my experience and passion to do great things here.
"It's wonderful to be back home in Liverpool and embarking on a unique journey like this. I hope I can do our club and our fans proud."
Moore, 62, brings with him a wealth of experience, having held senior positions with Microsoft, Sega and Reebok over the past two decades.
He will report directly to the club's owners, FSG, and his arrival now completes the senior management structure of the club.
Speaking on behalf of Fenway Sports Group principal owner John W Henry and chairman Tom Werner, president Mike Gordon said: "Finding an individual with the experience and gravitas to lead a unique organisation like Liverpool Football Club is no easy task, but in Peter Moore we believe we have the ideal person.
"It was critical to identify someone who could complement the extraordinary talent we have in our football leadership operation.
"During his distinguished career, Peter has demonstrated that he has the strength, vision, charisma and most importantly the experience of leading a global enterprise and moving it forward.
"With his decades of extensive business dealings all over the world, he has a global reputation as a business leader.
"His value is enhanced by his deep-rooted connections to the city of Liverpool and the club itself.
"To have found - and now appointed - an individual who encompasses all the business and leadership skills, allied with an authentic local connection, that understands the distinct nature of this club, means he was our first and only choice and we're in no doubt his qualities and experience will help drive the club forward in a positive direction."