The Brazilian signed a five-year contract in a ceremony sitting alongside Barca president Josep Maria Bartomeu, making him the third-most expensive player in history.
"It's an honour for me, a great honour, but also a dream to be here," Coutinho said after posing on the Camp Nou pitch in a Barcelona shirt.
"I have my goals; to get here, to be happy, win titles and have fun -- I only think about that."
Minutes before the 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.
The runaway La Liga leaders also claimed that Liverpool had cut their original asking price from 200 million euros, after a long-running transfer saga dating back to the summer window.
"Due to a contractual issue and due to Liverpool's desire, we cannot provide the exact figures, but there has been a very significant reduction (in price)," said Barcelona vice-president Jordi Mestre.
Barca's swoop for Coutinho is outranked only by Paris Saint-Germain's stunning world record 222 million-euro signing of Neymar from Barcelona last year, and the Paris club's capture of French striker Kylian Mbappe in a deal which will be worth 180 million euros when the teenager completes his initial loan deal later this year.
Coutinho's arrival will help Barcelona move on from the humiliation of losing Neymar, and his presence alongside Lionel Messi and Luis Suarez will help take the pressure off another of the club's stars, 33-year-old midfielder Andres Iniesta.
But the Brazilian international insisted he would not be replacing Neymar or Iniesta in Ernesto Valverde's side.
"Neymar is a huge player... But we have different characteristics and I've come here to find my space," Coutinho said.
"I spoke with him. He told me about the city, the players and told me that this club has an amazing dressing room.
"Iniesta, for me, is a genius. What I like most is being in the group and being able to play, the rest is a question for the coach."
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 made three bids for Coutinho last year, but Liverpool stood firm.
In the end, the lure of a huge profit on a player they paid just £8.5 million for when he joined from Inter Milan in 2013 proved too strong for the English club.
- A good fit -
Coach Valverde predicted Coutinho will comfortably fit into his star-studded team, and he could now make his debut at home to Alaves on January 28.
Coutinho played with Suarez for 18 months at Liverpool before the Uruguayan made the same move to Spain in 2014.
"It's an honour to be able to play with him (Suarez) again," Coutinho added.
"He's helped me a lot, wrote to me a lot and explained to me about the club and city... He even visited a few houses for me! He's a very close friend."
Valverde admitted that it would be a challenge to find a position for Coutinho, with the Spanish title looking a formality and the player cup-tied for the Champions League.
"I have seen him play in various positions -- on the right, the left, in the middle, on the wings," said Valverde.
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.
His departure is a blow to Liverpool as he had returned to top form after an injury-hit start to the season, scoring seven goals in the last eight games of 2017.