Setien, who most recently served as the manager of La Liga's Real Betis, received a contract that runs through June 30, 2022.
Catalunya Radio and Onda Cero (h/t Football Espana) each previously reported the Spanish champions had begun negotiations with Valverde over his exit. His contract was not due to expire for five more months.
The 55-year-old, who represented Barca as a player, is set to part ways with the Blaugrana after they lost 3-2 to Atletico Madrid in the Spanish Super Cup semi-finals on Thursday. His side lead La Liga on goal difference, but confidence in his ability has depleted.
Barcelona were recently hit by the news that striker Luis Suarez will be out of action for four months. A club statement said he underwent surgery following an injury to the "lateral meniscus in his right knee" (h/t Reuters).
Valverde's side successfully retained the league title last season but lost 2-1 to Valencia in the 2019 Copa del Rey final.
Barcelona also fell short in the 2018-19 Champions League, letting a 3-0 first-leg lead slip against Liverpool in the semi-finals. It was a second wasted opportunity in Europe on Valverde's watch after his side were knocked out by AS Roma in the last eight of the previous campaign despite winning the first leg 4-1.
The tactician arrived at the Camp Nou in 2017 after impressing during his second stint in charge of Athletic Bilbao. Valverde also previously managed top-flight teams Valencia, Espanyol and Villarreal.