The decision to remove Valverde was confirmed following a board meeting that lasted more than four hours at Camp Nou on Monday afternoon.
Barca are top of La Liga but have won only one of their last five matches. Valverde is the first coach the club has sacked mid-season since Louis van Gaal in 2003.
“FC Barcelona and Ernesto Valverde have reached an agreement to terminate the contract that united both parties,” read a club statement released on Monday night.
Setien will be presented in a press conference at Camp Nou at 2.30pm local time (1330 GMT) on Tuesday.
“Barcelona and Quique Setien have reached an agreement for the latter to become first team coach until 30 June 2022,” the club said.
“Setien is one of the most experienced coaches in Spanish football,” it added. “Throughout his career he has been a proponent of possession based, attacking football that has been attractive to the fans.”
His first game in charge will be at home to Granada on Sunday. Barcelona play Napoli in the last 16 of the Champions League next month and Real Madrid in the league at the start of March.