The 20-year-old signed a long-term contract with the Premier League side after passing a medical at their Melwood training complex.
He spent last season on loan with Barcelona B, scoring 11 goals, and he proved to be a creative force as well, setting up 17 further goals in his 38 appearances.
Reds boss Brendan Rodgers said: "We are all delighted that Luis has decided to join Liverpool.
"He has the correct footballing profile and mentality to be a Liverpool player.
"I look forward to working with him to develop his talent and he joins a group of young exciting players at our club."
Alberto represented Spain at U18 and U19 levels and made his debut for their U21 side against Belgium in February.
Alberto admitted he had been surprised when he became aware of Liverpool's interest, but had no doubts about accepting their offer.
"I feel like I'm in a bubble at the moment," he told the club's official website. "For me Liverpool is a top team. I feel like I am dreaming and I want to enjoy it to the full.
"I feel very excited, I've never felt so excited before but I'm very happy. I think I am the happiest man on earth.
"I was surprised [when Liverpool showed interest in me]. You never expect this to happen to you. But as the deal moved forward, I became very happy and wanted to come to Liverpool.
"I have come here to enjoy moments with the supporters - and I know the supporters will help me to never walk alone.
"I hope that between us all we can make this club one of the greatest in the world, once again."