The 22-year-old becomes the club's second signing of the summer as manager David Moyes continues to implement significant changes to his team ahead of the upcoming season.
Barry. joins after an outstanding debut season in LaLiga, where he scored 11 goals and provided four assists.
Moyes persuaded Barry to make the switch.
In an interview with the club's website, the 6ft 5in forward, who is expected to take over from Dominic Calvert-Lewin,expressed his excitement about joining the Toffees and fulfilling his dream of playing in the Premier League.
"I'm very excited. It's thrilling to be here. I can't wait to get started, and I hope to begin very soon.
"Everton is a prominent club in the Premier League. They have a rich history, and many great players have played here, such as Wayne Rooney and Romelu Lukaku.."
"When I was younger, I enjoyed watching these players; now I aspire to follow in the footsteps of those who came before me.
"I had positive discussions with the manager. He assured me that I possess the quality to compete in the Premier League. He wants to work well with me and assist me on my journey, and I sensed his sincerity, which is why I decided to come here.
"For me, playing in the Premier League is a dream. I believe I have demonstrated throughout my career that I can adapt.
"For instance, last season I joined LaLiga, which is a top league, and I think I had a successful first season. I'm not afraid to play here and achieve similar success."
Barry is eager to score in front of Everton's 'passionate' fans.
The Spanish club aimed to approach the £34 million release clause in Barry’s contract, but it has been disclosed that he joins for an undisclosed fee.
He elaborated on the enthusiasm of Everton fans and expressed his eagerness to score at their newly completed stadium next season.
"I think the fans here are quite passionate... I love this!" he stated.
"I enjoy scoring for these supporters. I just want to play here, score, and share the joy with the fans.
"On the field, I always give 100 percent; I always aim to score and help the team win. This is my nature. For me, scoring is like nourishment. When I score, I'm extremely happy. I will always give my all on the field and strive to find the back of the net.
"The stadium is enormous; it’s an incredible venue, and I look forward to seeing the fans there.
"When the manager arrived last season, I think he made some adjustments to the team, and I feel that along with the new stadium, the club is moving forward with fresh ambitions, so I want to contribute to that."
Moyes believes Barry possesses significant potential.
Finally, Moyes commented on the transfer and indicated that more signings are forthcoming.
"We are thrilled to have brought Thierno to the club. We see great potential in him, and we expect good things.
"We will provide him ample time to acclimate, and we look forward to beginning our work with him as soon as possible.
"I hope to make additional signings in the coming weeks."
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