Valverde has signed an initial two-year deal at Camp Nou, having elected to leave Athletic Bilbao to join the Catalan giants.
He was presented at Camp Nou on Thursday, having arrived in Barcelona the previous day – returning some 27 years after leaving following a two-year playing career.
“It’s a privilege to be at Barcelona and that they show great confidence in me,” said Valverde.
“When a team like Barcelona calls you, you don’t have to think about it too much. It is the most difficult challenge in my career, but also the most attractive and one of the best challenges [anywhere], of that I have no doubt.”
Valverde is looking forward to working with Lionel Messi next season, describing it as “a unique experience to train the best player I’ve ever seen on the field.”
And the ex-Athletic boss says club captain Andres Iniesta still has a vital role to play at the club.
The World Cup winner has just one year left on his contract and made only 13 starts in La Liga this season. As such his future is unclear, amid suggestions that the 33-year-old could potentially call time on his career in 2018.
Iniesta himself has said he will review things during the season, “depending on how the season goes, on what the club offers, on how I see it and also how they see it”.
Valverde has full confidence in his captain, stating: “I consider Iniesta to be a very important player for the team and for the club from all points of view.
“He can still bring a lot out on the field, but first I want to talk to him.”
The Liverpool star has been a long-time target of the club’s hierarchy, and impressed during a 13-goal season at Anfield.
A number of Barcelona players have spoken in the last 12 months of their keenness for Coutinho to head to Spain
But it’s suggested that Valverde doesn’t see how the Brazilian would fit into his side.