The gifted 23-year-old attacking midfielder is moving to Anfield from Germany's Hoffenheim, where he played since 2010, scoring 47 goals in 151 appearances.
No details were given regarding the transfer fee or length of contract, although the deal was reported to cost Liverpool around 28 million pounds.
Firmino has been outstanding at Hoffenheim, maturing from an exuberant teenager to team leader despite his young age and attracting the interest of several top European clubs in the process.
"The Reds have seen off serious competition from rivals in the Barclays Premier League and across Europe to make it Anfield where the goalscoring instincts and creative flair of Firmino can continue to blossom," Liverpool said in a statement.
"Liverpool had been watching all along and acted fastest to put together a deal for Firmino, who will be exhibiting his mesmerising skills at Anfield from August."
Versatile and skilled, Firmino can play a variety of roles in attack and midfield and his development in the past few seasons saw him earn a first Brazil cap last year.
He has also started Brazil's last two fixtures at the Copa America, scoring the winner against Venezuela as his country advanced to the last eight of the competition.
Following a disappointing campaign in which the club could only finish sixth in the league, Firmino is the latest player to join Liverpool in a hectic start to the summer transfer window after the departure of long-time captain Steven Gerrard.
Midfielder James Milner, striker Danny Ings and goalkeeper Adam Bogdan have all completed Bosman moves, while promising defender Joe Gomez joined the club from Charlton Athletic for 3.5 million pounds.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
