Liverpool have yet to confirm the length of the deal, but the playmaker is highly rated by the Reds and has already made eight senior appearances in all competitions this season.
And the boss of the Reds, Klopp, is delighted that the juvenile international from England has put the pen on paper.
“Brilliant news – really happy,” the boss told Liverpoolfc.com.
“Harvey is such an exciting prospect. We all know its qualities – we have seen them this season in the first team and in U23.
“I love his attitude – I love his enthusiasm – I love his bravery – I love the fact that he has the right dose of confidence and football nerve.
“I think the public may not yet know the real Harvey and that is partly because we have sought to protect him and to protect him.”
“But he’s such a nice, polite and humble boy – who appreciates the talent and the opportunities he has – and who loves football. He loves the game above all, would play every minute of every day if he could – and he also loves this club and it’s a good mix. ”
Klopp also described his long-term plan for Elliott and insisted that the youngster’s development will not be rushed.
The boss added: “What is essential – so important – is that we give it time and space to develop. He will get that from us. He must be able to make mistakes while he learns and not feel more pressure than what is right and just.
“He is young and he is still in the early stages of his development.
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“The great thing is that he has the perfect crop here and we will protect him. Senior players and coaches really care about him and are as excited about his future as I am. So we will all be part of its story as it unfolds.
“He wants to fulfill all of his football dreams at LFC. Brilliant. Because of his commitment to us, with this contract, we have a chance to see if we can achieve it together.
“We now have a shared responsibility. He must remain committed to learning and improving and we must ensure that he has the opportunity. “