He had been widely expected to take over at Barca from the departing Luis Enrique.
The 53-year-old played for Barcelona as a striker, scoring eight goals in 22 appearances between 1988 and 1990 under the guidance of the legendary Johan Cruyff
Valverde announced he would be leaving Athletic last week after four years in charge at the Basque club.
At a press conference, Barcelona president Josep Maria Bartomeu said the club had appointed Valverde for "many reasons."
"Valverde has the ability, the judgment, the knowledge and the experience," he said.
"He promotes the youth players and he has a Barca way. He has a philosophy that is similar to ours. He is a hard worker and he is a fan of using technology in training and in managing matches."
Valverde will be officially unveiled before the media Thursday.
Enrique secured nine out of a potential 13 trophies during a fruitful three years in charge at the Nou Camp, including two La Liga titles and the 2015 Champions League crown.
Yet although the Blaugrana secured a third straight Copa Del Rey title with a 3-1 victory over Alaves on Saturday, it has suffered a disappointing season by its own high standards.
Barca finished second in La Liga behind arch rival Real Madrid and exited the Champions League at the quarterfinal stage after being outclassed by Juventus.
Enrique announced in March that he would be leaving Barcelona.
Speaking to the Barcelona website
after the Copa Del Rey victory Saturday, Enrique said: "I feel happy because I have enjoyed a lot making Barca fans happy by winning trophies and that makes me proud.
"I am the one who has decided to stop because it will be the best for me and for the players, they need potent and intense stimulus. Nine trophies out of 13 is a pretty good record."
Valverde has enjoyed success as a manager.
He took Barca's crosstown rivals Espanyol to an unlikely UEFA Cup final in 2007 only to lose on penalties to Sevilla.
As manager of Olympiakos, Valverde won the Greek Superleague title in 2009, 2011 and 2012, as well as the Greek Cup in 2009 and 2012.
His most recent silverware was won when Athletic defeated Enrique's Barcelona 5-1 over two legs to claim the 2016 Spanish Supercopa.
Yet Valverde, who has also coached at Valencia and Villarreal over his 15-year managerial career, will be expected to challenge for honors immediately at a demanding Barca.
His first chance will come when Barca faces Real Madrid in the Spanish Supercopa in August.