“Mathieu will sign a contract with FC Barcelona for the next four seasons plus a further optional,” Barca said in a statement.
“The cost of the transfer is 20 million euros and the buy-out clause will be 50 million euros (39.5 million pounds).”
The 30-year-old Mathieu will bolster the centre of Barcelona's defence after they missed out on any major trophies last season and their porous backline was a significant factor.
The Frenchman, who can also play at left back, continues the restructuring of the squad under new coach Luis Enrique.
Striker Luis Suarez, midfielder Ivan Rakitic and keepers Marc-Andre ter Stegen and Claudio Bravo have also been signed.
Midfielder Cesc Fabregas and forward Alexis Sanchez have left for Chelsea and Arsenal respectively.
(Reporting by Tim Hanlon, Editing by Ed Osmond)
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