The Spanish forward, who spent last season on loan at Barcelona B in the Segunda Division, has signed a "long-term" contract after completing a medical at the club's Melwood training complex.
Alberto becomes the club's third signing of the summer after Kolo Toure arrived from Manchester City on a free transfer and Iago Aspas joined from Celta Vigo.
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Upon joining the club, Alberto told the Liverpool website: "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 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."
Manager Brendan Rodgers was equally as excited about securing another talented youngster and told the club website: "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."
Managing Director Ian Ayre added: "Luis was top of the list in terms of his ability and skills in the position he plays in.
"He's a very exciting player and I know Brendan is very excited about it. So hopefully our fans can be too."
Alberto, who made just seven appearances in La Liga, racked up an impressive 11 goals and 17 assists during his season-long stay with Barcelona B, where he made 38 appearances.