Arscott, 24, made a total of 36 appearances, scoring 80 points, during his time at Sixways and played a leading role in helping the club win promotion back to the Premiership in 2010/11.
Arscott began his career with his hometown club Plymouth before joining Bristol in 2007. In his three seasons at Bristol he scored 20 tries in 69 appearances.
Capped by England at Under 19 during his time at Plymouth, Arscott has also represented England Saxons.
"The big appeal in joining London Welsh for me was the brand of rugby," said Arscott. "For the last few years the club has been playing a really good style of rugby.
"They've got a good pack of forwards and a set of skilful backs, who enjoy throwing the ball around and having some fun out on the pitch.
"There is a step up from the Championship to the Aviva Premiership but over the last two or three seasons the gap at the top of the Championship and the bottom of the Aviva Premiership has narrowed.
"We'll definitely be looking to compete. We've got a good pre-season planned and the boys are already putting in a lot of hard work, and looking to get ourselves ready."