The attacking midfielder was given his first-team debut by Brendan Rodgers last month and has since gone on to start twice in the Premier League.
"I am really happy," he told the club website. "Liverpool are one of the biggest clubs in the world and this is the right place for me.
"I am happy Brendan has shown trust in me. I had no questions about signing a new deal and I am really glad to have done so.
"I am comfortable here. I have played some games for the first team and I hope to continue doing that, but I need to work hard every day for that to happen. This is one of the best days of my life."
Rodgers said: "At 18, Suso has demonstrated outstanding technical qualities but also shown very good temperament to play for such a prestigious club.
"His commitment is very good news for all our young Academy players and the excellent work taken place by the Academy coaches and staff."
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