Moore will step down from his role overseeing the club’s off-pitch business operations at the end of August, following the completion of his three-year contract.
The Liverpool-born executive had spent more than three decades living in the US until his appointment at the football club in 2017.
In a statement, Moore confirmed he would now return his home in the San Francisco Bay area.
“I came back to Liverpool in 2017 having been in the US for over 30 years and it’s been such a special experience,” he said. “My wife and I married here two years ago and we go back to the US to our families with mixed emotions.
“Excited and looking forward to being reunited with our families and grown-up children in the US, emotional about leaving Liverpool which we’ve loved every minute of the opportunity to make a difference and leave our mark in the history of this great city and club.”