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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.