He also won the FIFA World Cup with Germany in 2014.
Muller unofficially added an Olympic gold medal to his list of honours on Tuesday when Germany's Christian Kukuk won the individual jumping equestrian event at Paris 2024 on board a horse called Checker.
That horse is part owned by Muller, who took to Instagram to celebrate this week.
Kukuk was riding a horse called Checker, who is part-owned by football star Thomas Muller
Muller uploaded a video of himself to the social media network. In it, he was wearing his gold medal from the 2014 World Cup, while a small stuffed toy horse was perched on his left shoulder.
'It's golden - we are Olympic winners,' declared Muller, who tagged Kukuk and the Beerbaum Stables in his post.
'Hats off to what you have done with Checker in the last year and a half. I am so excited. Let yourself go and celebrate now.'
Muller retired from international football earlier this summer after featuring in two of Germany's five games at Euro 2024.
He called time on his Germany career having scored 45 goals in 131 senior international appearances since 2010.
Muller is now preparing for his 17th consecutive season in Bayern's first team.
After missing out on the Bundesliga title for the first time in 12 years last season, Bayern will begin their bid to win it back on August 25 when they kick off the new campaign with a trip to Wolfsburg.