But injuries combined with the form of fellow Red Rose No.10 Toby Flood and Jeremy Staunton has seen the 28-year-old fall down the pecking order at Welford Road this season.
Vesty - a fourth-generation Tiger - racked up 164 appearances for Leicester during a 13-year spell but has pulled on the first team jersey just six times in the 2009-10 campaign.
And he says he cannot wait to unleash his attacking instincts at the Rec.
Vesty said: "I am really looking forward to coming to Bath. They appealed to me because of the exciting brand of rugby that they play.
"They like to get the ball into space and attack with ball in hand which is a style that suits and excites me."