The Catalan giants sealed a €20 million deal for the centre-back on a four-year contract from Valencia on Tuesday after weeks of negotiations between the two sides.
And Giuly - who played for Barcelona between 2004 and 2007 - insisted that Mathieu will be a strong addition at the heart of the club’s back line next term, filling the void left by fellow Frenchman Abidal in 2013.
"Mathieu is a good player. I played against him in France and Spain," Giuly told Mundo Deportivo. "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."
Giuly started his career in France with Lyon and Monaco before making the switch to Spain where he won two La Liga titles, one Champions League trophy and two Supercopas de Espana at Barcelona.
During his second season at the club, Giuly competed for his place in the side against a young Lionel Messi - who he thought then would develop into one of the best players in the world.
"We all knew Messi would be the player he is now," he said. "We knew he had an incredible talent and was going to grow. It's a dream to play with him. I still have a friendship with him."
Barcelona only won the Supercopa de Espana last season, with rivals Real Madrid clinching their 10th Champions League crown and the Copa del Rey title while Atletico Madrid were named 2013-14 league winners.
Despite their unsuccessful campaign last term, Giuly believes that while Barca "cannot always win" the Catalan giants will thrive under Luis Enrique this year.
"There are many changes in football, but they must be good for the future," he said. "I see a strong team and, with new coach Luis Enrique, I’m sure he’ll do a good job."