Having spent 16 years with the Reds, the midfielder joins Serie A side Internazionale in a permanent transfer, subject to international clearance.
Jones made more than 200 appearances for the club, scored 22 goals and lifted six major honours – including two Premier League titles.
He wrote on social media: “After 16 years, it’s time to say goodbye.
“I came here as a kid with a dream of playing for Liverpool, and I’ve been lucky enough to actually live that dream.
“This club is all I’ve ever known. I came here as a kid and I’m leaving as a man with a family of my own, which probably puts into perspective just how much of my life I’ve spent here.
“So much has happened during my time here, both on and off the pitch. I’ve made my debut, won trophies, made memories I’ll never forget, and I’ve become a dad.
“Having my daughter while I’ve been here makes it even more special because Liverpool isn’t just part of my story anymore, it’s part of my family’s story too.
“I want to thank everyone in the Academy who believed in me and helped me get to where I am today. There are people here who have known me since I was a kid and literally watched me grow up.
“Thank you to every manager and coach I’ve worked with for trusting me, giving me opportunities and always pushing me to become better.