Setien proved a surprise appointment as Valverde's replacement, after Xavi and Mauricio Pochettino had been touted as the top candidates for the job.
Valverde took training on Monday morning but his future looks bleak, with the club expected to announce his departure following a board meeting in the afternoon at Camp Nou.
They instead settled on Setien, handing the former Real Betis boss a contract until 2022 - although there is a break clause in 2021 due to club elections - and Bartomeu made clear he is hoping for instant results.
While coach at Las Palmas, he is also reported to have said that "I never really understood the game until I saw Cruyff's Barcelona play".
Xavi, now the coach of Qatari team Al-Sadd, indicated he is not prepared to take charge immediately but the negotiations left Valverde in limbo. He said he always dreamed of one day coaching Barcelona but was committed to Al-Sadd for now.
Messi and Valverde did not necessarily enjoy the best of relationships, with cheeky fans suggesting the 32-year old had previously saved his coach's job on numerous occasions with his performances on the pitch.
It felt like last season would have been the final straw when Barca blew a 3-0 lead in the Champions League semifinals to eventual champion Liverpool and fell short to Valencia in the Copa del Rey final.
Ever since that Anfield debacle, Valverde was on borrowed time in the Barca hotseat.
Nicknamed "El Maestro", midfielder Setien started out at hometown club Racing Santander in the 1970s before moving to capital giants Atletico Madrid, where he spent three years.
Valverde, 55, joined Barcelona in 2017. The Champions League matches against Napoli will be on February 25 and March 18. The first break for the experienced coach finally happened with Lugo, where he guided them to the Segunda Division and kept them there before departing for Las Palmas - who were in LaLiga - and leading them to survival. It hasn't won the European competition since 2015.
"Quique Setien will be the new FC Barcelona coach".
Barcelona's next game is on Sunday at home against Granada in the Spanish league.