Achterberg posted to social media: "After 15 years at the club, I have decided with a heavy heart to leave LFC.
"It has been an unbelievable and great journey for me and my family. I have loved each day working at this amazing club, but after a long think I feel it could be right for me to start a new challenge.
"I would like to thank FSG for all the support during those 15 years Mike Gordon, John Henry, Tom Werner and Billy Hogan. It has been a privilege to work for the biggest and greatest club in world football with its amazing supporters. Whether they are Scouse or non-Scouse, I loved them all worldwide.
"A massive thank you goes to our manager Jrgen Klopp. What joy he gives to all of us. Klopp has fulfilled all our dreams at LFC. He is one of (the) best managers in the history of the city, the club and world football.
"He created world-class teams with his man-management skills, he brought us back to being believers, winners, and a force in European and world football.
"For me personally, I cannot thank him enough for everything he has done for me and my family, for the trust he gave me to do my job to the best I can, the joy, inspiration and the great leadership."