The 28-year-old joins on a free transfer after leaving Luton this summer and training with the Robins during pre-season.
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Adebayo becomes City’s 10th signing of the summer and will wear the No. 45 shirt.
“I can’t wait to get started. The place has a feel-good factor and it has been easy for me to settle in,” he told the club website.
“The gaffer has been very clear with what he wants from us and how to attack the season so that is a big reason why I wanted to join.
“I will try and use my experience to push the group and get everyone going in the same direction.”