The 20-year-old Spaniard has penned a long-term deal for an undisclosed fee with the Premier League club.
"We are all delighted that Luis has decided to join Liverpool," manager Brendan Rodgers told the Reds' official website. "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, who joined Sevilla's academy in 2004, spent last season on loan at Barcelona B.