Mathieu arrived from La Liga rivals Valencia on Wednesday for a fee of €20million, which raised eyebrows in some quarters.
The 29-year-old joins with the intention of shoring up Barca's central defensive options, after the retirement of Carles Puyol last season and Gerard Pique's injury troubles.
Giuly, who played for the club between 2004 and 2007, believes the Frenchman will be a hit at the Catalan giants.
"Mathieu is a good player," he told Mundo Deportivo. "I played against him in France and Spain.
"He's a strong player that can provide pace for Barca in defence.
"He might provide what Eric Abidal gave to Barcelona but much tougher.
"His price is a little high, but this is up to the clubs. The player should be focused on playing for his club and that has nothing to do with the price."