Valverde was relieved of his duties on Tuesday morning after two and a half years at the Camp Nou, with four major titles won since his arrival from Atheltic Bilbao.
The Spaniard came under increasing pressure after shock UEFA Champions League exits at the hands of AS Roma and Liverpool and fans becoming vocal of the squad's playing style.
And after a public pursuit of club legend Xavi and Netherlands boss Ronald Koeman that begun last Friday, Valverde was finally axed and replaced by former Real Betis boss Quique Setién.
"My time as FC Barcelona coach has come to an end. It has been an intense two and a half years right from the start," Valverde wrote, which was published on the club's website.
"In that time I have enjoyed some joyful moments celebrating victories and trophies but also others that have been tough and difficult.
"However, above all, I would like to highlight my experience with the fans and the affection showed towards me during my time as coach.
"I would like to thank the president Josep Maria Bartomeu and the Board of Directors for giving me the opportunity to coach the first team and their confidence during all this time.
Valverde added: "I would also like to thank all the people I have worked with at the Club for their support and how they treated me during the two and a half seasons, especially those who work in and around the first team and with whom I have shared so many moments at the Ciutat Esportiva and during away trips.
"Of course, I would like to thank the players for all their efforts that have allowed us to claim four trophies together. From this day, I wish them all the luck in the world and to the new coach Quique Setién also.
"All the best to everyone, Visca Barça and Visca Catalonia, Ernesto Valverde."