Coutinho, 25, signed a five-year contract in a ceremony sitting alongside Barça president Josep Maria Bartomeu before posing on the Camp Nou pitch in a Barcelona shirt.
"I am very happy to be here. This is a dream come true and I hope to meet everyone's expectations on the pitch," Coutinho said.
Minutes before the Brazilian midfielder put pen to paper after a whirlwind few days, the club said a thigh injury would delay his debut until the end of January.
Barça's swoop for Coutinho is outranked only by Paris Saint-Germain's stunning world record €222 million signing of Neymar from Barcelona last year, and the Paris club's capture of French striker Kylian Mbappe in a deal eventually worth €180 million.
His arrival will help Barcelona to move on from the humiliation of losing Neymar to Qatar-backed PSG, and his presence alongside Lionel Messi and Luis Suarez will help take the pressure off another of the club's stars, 33-year-old Andres Iniesta.
Bartomeu said the club had secured "one of the stars of world football" and admitted that Liverpool had put up a fight to keep the player.
"It was not easy and other clubs expressed an interest in him, but he was determined to come here," the president said.
Barcelona had made a bid for Coutinho in the summer, but Liverpool stood firm.
In the end, the lure of a huge profit on a player they paid just £8.5 million when he joined from Inter Milan in 2013 proved too strong for the English club.
A good fit
Coach Ernesto Valverde predicted Coutinho will comfortably fit into his star-studded team.
He could now make his debut at home to Alaves on January 28th.
Coutinho played with Suarez for 18 months at Liverpool before the Uruguayan made the same move to Spain in 2014.
"Everybody knows about his quality. He has been playing at the highest level for years now and that is important," Suarez said.
"Now we need to make sure he feels at home because we know that changing club is always difficult, but I think he is the type of player who will fit well into the team."
Valverde admitted that it would be a challenge shoehorning his new recruit into a squad already running away with the Spanish league title.
"Coutinho is a player who I think can bring a lot to us," said Valverde. "He's an important signing."
"I have seen him play in various positions -- on the right, the left, in the middle, on the wings."
The timing of Barça's move for Coutinho has been questioned because he will not be able to play in the Champions League this season having already played in the competition for Liverpool.
But he is likely to be used to give Iniesta a rest, keeping the veteran midfielder fresh for the Champions League as Barcelona seek to wrest the trophy back from bitter rivals Real Madrid.
Rio-born Coutinho scored 54 goals for Liverpool in all competitions, although he won no silverware during his five-year stay at Anfield and he never made a secret of his desire to move to a club where Brazilians such as Ronaldinho and Romario have shone in the past.
His departure now is a blow to Liverpool as he had just returned to top form after an injury-hit start to the season, scoring seven goals in the last eight games of 2017 to put his side firmly in the Champions League places.
"It is no secret that Philippe has wanted this move to happen since July, when Barcelona first made their interest known," Liverpool manager Jurgen Klopp said at the weekend.
"Philippe was insistent with me, the owners and even his teammates this was a move he was desperate to make happen."
Liverpool have been tipped to quickly reinvest their windfall from the Coutinho sale.
Despite already paying Southampton £75 million for defender Virgil van Dijk, Klopp will be chasing an attacker with Leicester City's Algerian winger Riyad Mahrez and Monaco midfielder Thomas Lemar already linked with a switch to Anfield.
By Daniel Bosque and Jean Decotte / AFP