According to media reports, the deal will keep him at Anfield until 2020.
Coutinho, 22, has made 81 appearances since joining from Inter Milan in 2013 and has been one of Liverpool's most impressive performers over the last two seasons.
"It means so much. This club has given me the opportunity to play and believed in me even though I hadn't been playing regularly at my previous club," he told the Anfield team's website.
"Liverpool is a big family and I'm a happy person here."
Manager Brendan Rodgers said there was even more to come from Coutinho.
"The most exciting thing isn't just how good he is now, it's the further improvement he can make in his game. In terms of potential he can still become even better," said Rodgers whose side are seventh in the Premier League.
(Reporting by Martyn Herman, editing by Tony Jimenez)
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