The Telegraph reports the new deal will keep him at the club until 2023.
The 26-year-old signed his new deal having thoroughly impressed this season under Jurgen Klopp, scoring 26 goals and recording 13 assists in all competitions as one key component to Liverpool's attacking triumvirate - one that Manchester City manager Pep Guardiola called "almost unstoppable."
Chris Bascombe of the Telegraph adds that Firmino's deal is worth a reported £9 million a year, making him Liverpool's highest-paid player at £180,000 per week. Firmino said signing his new contract "was an easy decision."
"The club have taken me in in an incredible way and I've grown a lot here with my work with the support of the whole team. I am very, very happy here," Firmino said in a club-issued statement.
"Everything fits in the best possible way. My teammates are fantastic and I am very grateful to be able to play with them at this club.
"I love to play for Liverpool FC. The fans are excellent and fantastic in how they support us all the way. They support us throughout the games and the work they do during the match is beautiful."
Since joining Liverpool out of 1899 Hoffenheim in 2015, Firmino has been a regular fixture in the Reds' lineup, making 140 appearances and scoring 50 goals over the last three seasons. Firmino made his 100th Premier League appearance earlier in the month in a 2-2 draw against West Brom, and has worked his way back into the conversation for a starting role with Brazil during the 2018 World Cup.
Before the Russian affair kicks off in June, however, Firmino will be afforded another chance to shine on a grand stage as Liverpool takes on AS Roma in the second leg of the Champions League semi-finals, having commanded a 5-2 lead in the first leg. As expected, Firmino was also on the scoresheet, having scored a pair in the second half to compound Roma's misery at Anfield.