The Frenchman, 29, moved from Valencia on Wednesday, and was officially presented as a Barcelona player on Thursday.
Barcelona's issues in the centre of defence were well documented during 2013-14 after injuries to Carles Puyol and Gerard Pique.
Critics of the club claimed their timing of signing Mathieu was too late, plus their fee is exorbitant for a player on the brink of 30.
But Mathieu expressed his delight at the transfer, after five years at Mestalla with Valencia.
"It's a huge pleasure to be able to play for Barcelona, for me it is the biggest club in the world and I'm very proud and happy to be here," he said.
"I'm a versatile player but I feel most comfortable at centre-back and I've come to the club to play centre-back.
"Coming here is the result of the work I've done throughout my career. I've worked so hard to be here, maybe this chance is coming late in life but here it is and I'm going to try and enjoy it as much as I can.
"They've been after me for some time and I thank them for their confidence, since they first got in touch, I've done everything I can to come here
"Now it's a fact, it's a joy and I'm very, very happy.
"I'm the kind of player that always assumes responsibility, I always do the best that I can and give 100 per cent for the club, whichever club I'm at."