Flick, who has not managed a club since being sacked by Germany in September 2023, will be tasked with reviving Barcelona's fortunes after the Catalan side failed to win any trophies this season under Xavi, who was dismissed on Friday.
In a statement, the club said it had "chosen a man well known for his teams' high pressing, intense and daring style of play which has brought him great success at club level and international level, winning pretty much all there is to win in the world of football."
Flick said it was an honour and a dream to be the Barcelona coach.
"I'm really looking forward to start working for this amazing club. Since I have arrived I have seen that everyone loves this club and does everything they can for its success," he told Barca TV.
"In the first team, there is a good mix of experienced players and talented young players. I think we have to work to be able to improve... I won a few titles with Bayern Munich and I'd like to continue this path at Barcelona."
Barcelona highlighted the German's success during the 2019/20 season at the helm of Bayern, with whom he won six trophies - the Bundesliga, the German Cup, the Champions League, the German Super Cup, the UEFA Super Cup and the Club World Cup.
Xavi was sacked last week after a trophy-less season in which Barca finished 10 points behind champions Real Madrid, lost the Spanish Super Cup final to their arch-rivals and were knocked out of the Champions League by Paris St Germain in the last eight.
Xavi originally announced in January that he would leave following this season but then later agreed with the club to see out his contract, which ran until the summer of 2025. However, last week, the club management decided to end his contract early after all.
Prior to Flick's announcement, the club released a statement announcing the decision to sever Xavi's contract.
"The club wishes to publicly thank Xavi and the rest of his coaching staff for their commitment, dedication and generosity, and for their help in reaching an agreement to sever the contract.
"Furthermore, we wish him success in the future on both a personal and professional level," the statement read.