The 37-year-old, who previously spent time with Wasps, joins from Super Rugby outfit Queensland Reds.
Bristol have handed the back-row a short-term, six month contract as they look to provide injury cover for Jake Heenan, Sam Graham and Dan Thomas.
Smith will offer plenty of experience and Bristol head coach Pat Lam believes he is a perfect fit for their playing style.
He told BBC Radio Bristol: "It's fantastic for Bristol Bears to bring in someone of that quality and experience. Someone of George's reputation is perfect for us.
"Dan Thomas - who had a phenomenal season last year - took a bad knee injury and is not expected back until about October, possibly November.
"Then, in the last game of the season, we lost Sam Graham, our academy number seven. He's going to be struggling for the beginning of the season.
"Jake Heenan is recovering and will be coming back from a long-term shoulder injury, and then in November, Jack Lam is going to be tied up with international duty."