The contract details and transfer fee have not been disclosed by either club.
Time for change
This is the first time that the 21-year-old goalkeeper will have switched sides, having spent an incredible 14 years throughout the Stuttgart youth ranks.
He arrived when he was just seven from VfL Wangen, and has since risen up the ranks with the Swabian giants.
Vlachodimos has made the most of the time with Stuttgart, earning three first-team appearances and a call-up to the Germany under-21 side this term.
However, competition from the two first-choice goalkeepers has proven too much and - given the age he is - playing minutes are a priority.
No second chance
With both Mitchell Langerak and Przemyslaw Tyton as the two top stoppers, it initially looked likely that he would continue to play for Stuttgart's reserves.
However, ironically, it is with his under-23 manager, Jürgen Kramney that he was not given a further chance to shine despite the debatable form his Polish counterpart.
Now that Langerak has returned to fitness, it is up to the two custodians signed in the summer to do battle for the number one shirt.
Dutt thanks the 'keeper for his service
Sporting director Robin Dutt thinks that it is a good move, "In Panathinaikos, Odi has found an attractive and interesting, tradition steeped club at which to make the next step in his career.
Speaking to the club website, he added: "We thank him for his efforts here at VfB and wish him all the very best for his future."
Stuttgart are in action again this weekend after returning from their winter break with an impressive 3-1 win over 1. FC Köln, and take on Hamburger SV this Saturday.