The 19-year-old scored on his senior debut against Young Boys in September and has gone on to make 14 first-team appearances for the Reds so far this term.
He told the club's official website: "It's a great honour to sign a new contract at the club and I'm very happy.
"It was an easy decision to make - as soon as they offered it to me, I grabbed the opportunity with both hands because it's a great club and I just want to continue to play for Liverpool.
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"There's still so much hard work ahead. There is big competition within the team and everyone wants to play football. I just hope I can keep progressing and continue in the way I have been."
Liverpool's managing director, Ian Ayre, hailed the deal and believes the future at Anfield is bright after recently also securing Raheem Sterling to a long-term deal on Merseyside.
Ayre added: "It's fantastic news. It's another great example of a player committing to the club and what we're trying to achieve under Brendan [Rodgers].
"He's a great young player, shown a fantastic improvement, broken into the first team and made a huge contribution - and rightly so, we've provided him with a new contract and a long term one.
"Getting talent like him, Raheem and others to commit at this point is absolutely essential to the future.
"The manager, the owners and everyone have said the key is to build something for the long term - and young players are a catalyst to that. None more so than Andre.
"He's come on leaps and bounds in the last year or so and that's because of all the hard work he's put in and the manager giving him a chance, so it's absolutely essential players like that commit themselves to the club."