Ribery, 36, and Robben, 35, will both leave the club at the end of this season after a decade of unprecedented success.
Others such as Thomas Mueller, Manuel Neuer and Jerome Boateng have also been key figures in Bayern's treble-winning golden generation, but it is Robben and Ribery who stand out.
"Franck and Arjen are great players who shaped the most successful decade in Bayern's history," said club CEO Karl-Heinz Rummenigge in May.
Flying Dutchman Robben announced his departure in December, but remained injured for much of the season before returning to standing ovations against Hanover earlier this month.
A day later, Ribery confirmed that he too would be leaving the club at the end of the season, ending a 12-year spell in which he has won 22 titles.
Ribery, who has a close relationship with both the fans and club president Uli Hoeness, said in May that Munich would "always be my home".
Ten of his 12 years were spent playing alongside Robben, who joined Bayern from Real Madrid in 2009.
The Dutchman didn't immediately know whether he would take to life in Munich.
"At the time I was sceptical," Robben told the club website last year. "Now I know that it was the best decision of my career."
For the following decade, Robben and Ribery electrified the Allianz Arena on opposing flanks, earning the joint nickname "Robbery".
"We clicked with each other from the first day," said Robben last week.
Together, they laid waste to dozens of defences in a pincer movement of pace and quick feet, the left-footed Robben cutting inside from the right flank while right-footer Ribery did so from the left.
Bust-up and Wembley triumph
Their relationship, though, was not always easy.
In April 2012, Ribery punched Robben in the dressing room after a dispute over who would take a free-kick, and the Dutchman later admitted that he thought they would never play alongside each other again.
A year later, they had buried the hatchet as Bayern won an historic treble and Ribery set up Robben for an 89th-minute winner over Borussia Dortmund in the 2013 Champions League final at Wembley.
That season confirmed the lasting legacy of the "Robbery" era: Bayern's return to the very top of European football.
When Robben joined the club in 2009, it was nearly a decade since Bayern had last reached the Champions League semi-finals.
Since then, they have made the last four in seven of the last ten seasons, and appeared in the final in 2010, 2012 and 2013.
After Saturday's triumph, Robben and Ribery have now won eight Bundesliga titles together, and are aiming for a fifth German Cup next weekend.
Ribery, who also won the double in 2008, is now the only player in Bundesliga history to have won nine league titles.
In latter years, they have faced a constant battle with injury, with both of them having missed over 100 games for Bayern since 2013.
Yet despite age and injuries, both Robben and Ribery have managed to stay at the highest level for a remarkably long time, and are only now making way for successors Kingsley Coman and Serge Gnabry.
Ribery has become a mentor figure for fellow Frenchman Coman, just as he had been for his close friend David Alaba earlier in his career.
"Kingsley and Serge are doing really well already, and I hope they can achieve the same success as me and Arjen," said Ribery in May.
It has been a golden decade for Bayern, but now, the curtain must fall on the age of Robbery.