The defender was unveiled at Camp Nou on Thursday and said that Luis Enrique has had the move in mind for several weeks.
The 30-year-old has signed a four-year deal with the option of an additional season, with Valencia reluctantly agreeing to sell one of its prized assets for 20 million euros.
"Joining Barca is a reward for my whole career," he told the media at his unveiling. "I worked very hard to get here. The chance comes maybe a bit late, but I'll enjoy it. I did everything to join Barcelona, it's a joy to be here. I'm very motivated, I've come here purely to win trophies."
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Mathieu spoke with excitement about the next phase of his career and revealed he had spoken to former Valencia teammate Jordi Alba and new boss Luis Enrique even before the transfer was agreed to.
"Jordi Alba insisted that I join," he told reporters. "He said it's a great club and that I would feel good here. I spoke to Luis Enrique a month ago — he wants me to play as a center back and showed that he really believes in me. I like Barcelona's game because I like to play football. Just kicking the ball away is not really my thing."
Mathieu will wear the No. 24 shirt at Camp Nou and battle it out for a place alongside Gerard Pique at the heart of the back four, though he can also be used at left back.