Barca, which failed to find a buyer for the Frenchman, released Mathieu from his contract at the beginning of the summer market as he trained with Sporting.
Marca says Mathieu, just days later, inked terms with the Portuguese in a deal which also included a €2m signing on bonus.
The bonus was handed to the defender so to prevent him accepting rival offers from Fenerbahce or Marseille. Mathieu's deal also carries another €1m option if he renews the agreement.
Barca paid Valencia €20m for Mathieu in 2014.