The 33-year-old brings a wealth of experience to the club having been physiotherapist to the Scottish national team from 1999-2006, as well as to the British & Irish Lions on their tour to New Zealand in 2005.
He moves to Kingsholm from Guinness Premiership neighbours Worcester Warriors, where he has held the same post for one season.
"We've been extremely selective in our player recruitment to ensure that we only bring individuals of the highest quality to Gloucester Rugby, and that extends to our support staff too," said head coach Dean Ryan.
"Bob is one of the best physios in the game and we are very pleased to have him on board in one of the club's key positions.
"The unforgiving and relentless nature of club rugby, particularly in World Cup year, will stress even the biggest squads and the medical team are a critical factor in ensuring we are able to field our strongest possible XV every week."
Stewart added: "I obviously know [Gloucester coaches] Bryan Redpath and Carl Hogg very well from my time with the Scotland team, and I'm really looking forward to playing a part in what Gloucester are trying to achieve.
"Having spoken with Dean Ryan at length, I really associate with the elite and uncompromising environment he is driving at the club. If we can continue to provide the players with the best medical resources and support off the field, we can only enhance their chances off success on the field."
Stewart will oversee a medical team that includes senior physio Luke Anthony and new appointee Adam Brett, who joins Gloucester in his first full-time role in professional rugby after two seasons as Head Physio to National Division 2 side Henley Hawks.
In addition, following the retirement in June of Rob Mackay as club doctor after more than 10 years of service, Cheltenham-based GP Dr Chris Lamden will assume team doctor responsibilities, with Dr Rod Jaques - Director of Medical Services for the English Institute of Sport and sports injury specialist at Gloucester's Capio-Winfield Hospital - continuing to provide regular consultancy support.
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