He also helped Arsenal win the FA Cup and Community Shield during his time at the club, as well as reaching the 2006 Champions League final.
Arsenal paid tribute to the Reyes, saying: "Our thoughts are with all his family, friends and team-mates.
"Jose, who was part of the Invincibles team, was a hugely popular figure at our club and will always hold a special place in our hearts.
"He represented the club on 110 occasions, scoring 23 times and made memorable contributions to our 49-game unbeaten run.
"Rest in peace, Jose."
After leaving the north London club, Reyes joined Real Madrid on loan in the 2006/07 season, winning the La Liga title and later joined neighbours Atletico before returning to boyhood club Sevilla in 2012, going on to lift three consecutive Europa League titles between 2014 and 2016.
As well as lifting three Europa League titles with Sevilla, he was also part of the Atletico Madrid squad that won the competition in 2010 and 2012.
Atletico said in a tweet: "The Atletico de Madrid family is in mourning. Our former player Jose Antonio Reyes has passed away. You will forever be in our hearts. Rest in peace."
He later played for Espanyol and then Chinese club Xinjiang Tianshan Leopard before returning to Spain to join Extremadura in January.
His last match was a 1-0 win at Alcorcon on May 18. Extremadura are due to face Cadiz away from home on Sunday.
Tributes to Jose Antonio Reyes
Reyes' former Arsenal team-mates Thierry Henry and Ray Parlour took to Twitter to express their condolences.
Henry tweeted: "I'm devastated to hear the sad news about Jose Antonio Reyes. Wonderful player, superb team mate and exceptional human being. I wish his family and friends continued strength and courage to get through this difficult time. #takenfartoosoon."
Parlour added: "So Sad team mate of mine and great talent RIP Jose."
Real Madrid captain Sergio Ramos, who like Reyes came up through the youth ranks at Sevilla and was a team-mate of his with Spain and Real, tweeted his shock at the death of his friend.
The 33-year-old wrote in Spanish: "Broken. Destroyed. I have no words. All the love to the family. We'll always remember you, friend! RIP brother."
Scores of clubs across Spain and Europe also tweeted their condolences, including Barcelona who wrote: "FC Barcelona wishes to express their deepest condolences for the death of footballer Jose Antonio Reyes, a brilliant and charismatic player; one of the most outstanding figures and with a great trajectory in football. Rest in peace."
Portuguese giants Benfica, where Reyes played on loan for the 2008/09 season, added: "We're devastated to hear of the passing of our former player Jose Antonio Reyes. Our thoughts are with his family and friends. Rest in peace, Jose."
