"The player has signed a contract with the club for the next six seasons, ending on June 30, 2030, and his release clause is 500 million euros," said the Catalan side in a statement.
Playmaker Olmo finished as joint top scorer at Euro 2024 with three goals as he helped La Roja win the competition for a record fourth time.
The 26-year-old played for Barcelona at youth level before joining Dinamo Zagreb in 2014.
Attacking midfielder Olmo, who can also play on the left wing, signed for Bundesliga side Leipzig in 2020, where he won two German cups.
"A young club, a young player... we grew up, won our first trophies and made history together," said Olmo on social media network X.
"Thank you RB Leipzig, you'll forever be in my heart."
Olmo's arrival is the first under new Barcelona coach Hansi Flick, who was appointed in May following a disappointing campaign under predecessor Xavi Hernandez.
With Real Madrid winning La Liga and the Champions League before signing French superstar Kylian Mbappe, Barcelona start the new season as underdogs to Los Blancos.
The Catalans begin their La Liga campaign at Valencia on August 17.
Olmo's arrival leaves Barcelona with a host of midfielders, including Frenkie de Jong, Ilkay Gundogan and injured Spanish duo Pedri and Gavi.
