The experienced 30-year-old made 54 appearances during his stint at Gloucester before going on to become a key figure in the Leeds side.
Goodridge, who is also able to play on the wing, left Carnegie in 2010 and joined Esher - where he helped the club remain in the Championship.
And Bristol coach Liam Middleton is delighted to have signed the pacy back.
Middleton told the club's official site: "Jonny is a key addition to our backline options, he is an attacking fullback with good acceleration and brilliant counter-attack ability.
"He also brings a lot of experience, and is the right type of character for this squad. With Jack Tovey's ability to play at centre as well as in the back three and Sean Marsden and George Watkins having donned the 15 jersey this season, competition will be healthy.
"I've been impressed by Jonny's intense determination and that's a big part of what I'm looking for from my players this season."
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