Bale spent nine years with Real Madrid after joining from Tottenham Hotspurs for a then world record £85m in the summer of 2013.
His list of laurels at the Santiago Bernabeu included five Champions League titles, three La Liga trophies, one Copa del Rey, three UEFA Super Cups and three FIFA Club World Cups.
Although Bale's relationship with the Real Madrid fans deteriorated in his final years at the club, he still provided them with some memorable moments, including scoring in two UEFA Champions League finals.
Bale scored 106 goals in 258 games for Los Blancos, and the club have not forgotten these achievements in their tribute.
"Following Gareth Bale's announcement that he will retire from professional football, Real Madrid C. F. would like to express its gratitude, admiration and affection for a true legend of our club and the world game," it read.
"Gareth Bale was part of our team during one of the most successful periods in our history. He will long be remembered for his involvement in some of the most remarkable moments of the past decade, including his unforgettable run in the 2014 Copa del Rey final in Valencia [v Barcelona], his crucial goal in the 2014 Champions League final in Lisbon [v Atletico Madrid], and his brace in the 2018 Champions League final in Kyiv [v Liverpool], most notably the bicycle kick which will live forever in the minds of football lovers around the globe.
"His name will be forever bound to our club's history and its legend.
"Good luck, Gareth, and all the best to you and your family."