The 19-year-old goalkeeper - who trains with the first team at Melwood and made three friendly appearances for the senior side over the summer - committed his future to the club on Thursday afternoon.
“I’m very happy to sign a long deal with the club. I’m really enjoying my football here so I was happy to sign. Once the deal came in and I was happy, it was an easy decision really,” Kelleher told Liverpoolfc.com at Melwood.
“I’ve been doing the same things but getting better every day. Training at Melwood, you improve much more. Alisson and Simon and Kamil are here and we train to the highest level every day.