The Blaugrana were reportedly forced to part company with €20 million after weeks of tough negotiations with Valencia over the services of the centre-half.
Consequently, the Frenchman is determined to prove his worth to both his coach, Luis Enrique, and the fans as quickly as possible.
“Barca is the best club in the world and to go is a great opportunity for me," Mathieu confessed.
“I know how the club play their football and I have come to help bring quality to that.”
Mathieu represents the latest addition to a new-look Barcelona squad that has already been strengthened by the likes of Ivan Rakitic and Luis Suarez.